Editorial backlog

  1. Kaliev I.A., Sabitova G.S. The second boundary-value problem for the system of equations non-equilibrium sorption
    Status: reviewing
    Abstract.
    The second boundary-value problem for the system of equations non-equilibrium sorption
    Date of submission: 07 Avgust 2018 г.


  2. Kuznetsov D.F. Expansion of iterated Stratonovich stochastic integrals, based on generalized multiple Fourier series
    Status: reviewing
    Abstract.
    The article is devoted to expansions of iterated Stratonovich stochastic integrals of multiplicities 1-4 on the base of the method of generalized multiple Fourier series. Mean-square convergence of expansions for the case of Legendre polynomials as well as for the case of trigonometric functions is proven. Considered expansions contain only one operation of the limit transition in contrast to its existing analogues. This property is comfortable for the mean-square approximation of iterated stochastic integrals. Results of the article can be applied to numerical integration of Ito stochastic differential equations.
    Date of submission: 01 September 2018 г.


  3. On estimates for oscillatory integrals with phase depending on parameters
    Status: reviewing
    Abstract.
    In this work there are considered estimates for Fourier transform of measure, concentrated to analytic hypersurfaces, containing mitigating factor. In this paper it is given a solution of C.D.Sogge and E.M.Stein problem on optimal decaying of Fourier transform of measures with mitigating factor for partial class of family of analytic surfaces of three-dimensional Euclidian spaces.
    Date of submission: 08 October 2018 г.


  4. Benallia M., Realization of homogeneous Triebel-Lizorkin spaces with $p=\infty $ and characterizations via differences
    Status: reviewing
    Abstract.
    We study the commuting translations and dilations of realizations in the homogeneous Triebel-Lizorkin spaces $\dot{F}_{\infty,q}^{s}(\R)$, then we will give a characterization of the realized spaces of $\dot{F}_{\infty,q}^{s}(\R)$ via differences.
    Date of submission: 11 October 2018 г.


  5. Darus M., Dustov S.T., Lakaev S.N. Threshold phenomenon for a family of the Generalized Friedrichs models with the perturbation of rank one
    Status: reviewing
    Abstract.
    A family $H_\mu(p),$ $\mu>0,$ $p\in\mathbb{T}^3$ of the Generalized Friedrichs models with the perturbation of rank one, associated to a system of two particles, moving on the three dimensional lattice $\mathbb{Z}^3,$ is considered. The existence or absence of the unique eigenvalue of the operator $H_\mu(p)$ lying outside the essential spectrum, depending on the values of $\mu>0$ and $p\in U_{\delta}(p_{\,0})\subset\mathbb{T}^3$ is proven. Moreover, the analyticity of the eigenvalue and associated eigenfunction are shown.
    Date of submission: 06 November 2018 г.


  6. Abdo M.S., Panchal S.K., Wahash H.A. Fractional integro-differential equations with nonlocal conditions and $\psi-$Hilfer fractional derivative
    Status: reviewing
    Abstract.
    Considering a fractional integro-differential equation with nonlocal conditions involving a general form of Hilfer fractional derivative with respect to another function. We show that weighted Cauchy-type problem is equivalent to a Volterra integral equation, we also prove the existence, uniqueness of solutions and Ulam- Hyers stability of this problem by employing a variety of tools of fractional calculus including Banach fixed point theorem and Krasnoselskii’s fixed point theorem. An example is provided to illustrate our main results.
    Date of submission: 11 November 2018 г.


  7. Abdelwanis A.Y. ON TRIPLE DERIVATIONS OF PARTIALLY ORDERED SETS
    Status: accepted в т.0 №0
    Abstract.
    In this paper, as a generalization of derivation on a partially ordered set, the notion of triple derivation is presented and some fundamental properties are investigated for the triple derivation on partially ordered sets. Furthermore, it is shown that the image of an ideal and the set of fixed points under triple derivation are ideals under certain conditions. Finally, the properties of ideals and operations related with triple derivations are examined.
    Date of submission: 15 November 2018 г.


  8. Volchkov V.V., Volchkova N.P. A one-radius theorem on a sphere with pricked point
    Status: reviewing
    Abstract.
    We study functions on a sphere with pricked point having zero integrals over all admissible spherical caps and circles of a single fixed radius. For such functions a new one-radius theorem is established giving an injectivity condition of corresponding integral transform. An intermediate result of the article is strengthening of the well-known Ungar theorem on spherical means.
    Date of submission: 03 December 2018 г.


  9. Klimentov D.S. Stochastic analogue of the main theorem of the theory of surfaces for surfaces of bounded distortion and positive curvature
    Status: reviewing
    Abstract.
    Stochastic analogue of the main theorem of the theory of surfaces for surfaces of bounded distortion and positive curvature are under consideration. In this note a stochastic analogue of the Gauss--Peterson--Codazzi equations is derived and a stochastic analog of the main theorem of the theory of surfaces for surfaces of positive curvature of bounded distortion is given. In 1956, I.Ya. Bakelman derived the Gauss--Peterson--Codazzi equations for surfaces of bounded distortion. These surfaces are defined by functions with continuous first derivatives and summable with a square generalized second derivatives in the sense of Sobolev. In 1988, Yu.E. Borovsky proved that the Gauss--Peterson--Codazzi equations (derived by I.Ya. Bakelman) uniquely determine the surface of a limited curvature. The purpose of this paper is to present the results of I. Ya. Bakelman. and Borovsky Y.E. in the terms of the theory of random processes in the case of a surface of positive bounded distortion. With the help of two main forms of the surface, two random processes are constructed and the system of equations relating the characteristics (transition functions) of these processes is derived. The resulting system is a stochastic analogue of the system of Gauss--Peterson--Codazzi equations and is a necessary and sufficient condition for the uniquely determination of the surface (up to motion). Note that the generators of random processes are second-order operators generated by the main forms of the surface. For example, if the surface metric is given by the expression $ I = ds^2 = g_{ij} dx^i dx^j$, then the generator of the corresponding process is $ A = g^{ij} \partial_i \partial_j $. Next, a relationship between the transition functions of the random process and the generator coefficients is established. The obtained expressions are substituted into the generalized Gauss – Peterson -- Codazzi equations, which leads to the desired result.
    Date of submission: 25 December 2018 г.


  10. Garif'yanov F.N., Strezhneva E.V. On applications of summary equation induced by a quadrilateral
    Status: reviewing
    Abstract.
    A linear functional equation is investigated in the class of solutions that are holomorphic outside the quadrangle and disappear at infinity. A system of entire functions of a completely regular growth biorthogonal with a piecewise exponential weight system of degrees on three rays is constructed.
    Date of submission: 08 January 2019 г.


  11. Кокунин P.A., Чикрин Д.Е., Chuprunov A.N. ПРЕДЕЛЬНЫЕ ТЕОРЕМЫ ДЛЯ ЧИСЛА ЧАСТИЦ ИЗ ФИКСИРПОВАННОГО МНОЖЕСТВА ЯЧЕЕК
    Status: reviewing
    Abstract.
    Мы рассматриваем случайные величины - количества частиц в первых $K$ ячейках в неоднородной схеме размещения $n$ различимых частиц по $N$ различным ячейкам, где $K$ - фиксированное число. Мы показывает, что при некоторых условиях эти случайные величины ведут себя как независимые пуассоновские случайные величины. В честности, найдены условия, при которых суммы квадратов этих случайных величин, центрированных математическими ожиданиями и нормированных средними квадратическими отклонениями, сходятся по распределению к случайной величине, имеющей хи-квадрат распределение с $K$ степенями свободы, суммы этих случайных величин, центрированных математическими ожиданиями и нормированных средними квадратическими отклонениями, сходятся к гауссовской случайной величине с нулевым средним и единичной дисперсией. Даны приложения этих результатов к математической статистике.
    Date of submission: 24 January 2019 г.


  12. CIHAT DAGLI M. Some Relations On Universal Bernoulli polynomials
    Status: accepted в т.0 №0
    Abstract.
    In this paper, we derive a formula on the integral of products of higher-order Universal Bernoulli polynomials. As an application of this formula, the Laplace transform of periodic Universal Bernoulli polynomials is presented. Moreover, we obtain the Fourier series expansion of higher-order Universal Bernoulli function.
    Date of submission: 28 January 2019 г.


  13. Tursunov F.R., Of the Cauchy problem for the Laplace equation
    Status: reviewing
    Abstract.
    The article studies the problem of continuation of the solution and the stability estimate of the Cauchy problem for the Laplace equation in a domain $G$ by its known values on the smooth part $S$ of the boundary$\partial G$. The considered problem belongs to the problems of mathematical physics, in which there is no continuous dependence of solutions on the initial data. It is assumed that the solution to the problem exists and is continuously differentiable in a closed domain with exactly given Cauchy data. For this case, an explicit formula for the continuation of the solution is established, as well as a regularization formula for the case when, under these conditions, instead of the Cauchy data, their approximations are given with a given error in the uniform metric. We obtain estimates for the stability of the solution of the Cauchy problem in the classical sense .
    Date of submission: 04 February 2019 г.


  14. Babajanov B.A., Yakhshimuratov A.B. Integration of equation of Kaup system kind with a self-consistent source in the class of periodic functions
    Status: reviewing
    Abstract.
    In this paper, the inverse spectral problem is applied to the equation of Kaup system kind with a self-consistent source in the class of periodic functions.
    Date of submission: 25 February 2019 г.


  15. Shcherbina V.V. On the algebraicity of the lattice of $\tau$-closed totally $\omega$-saturated formations of finite groups
    Status: reviewing
    Abstract.
    All groups considered in the paper are assumed to be finite. The paper studies properties of the lattice of all partially closed functorially totally saturated formations which are related to the concept of being algebraic for a lattice of formations. We prove that for any subgroup functor $\tau$, the lattice $l_{\omega_{\infty}}^{\tau}$ of all $\tau$-closed totally $\omega$-saturated formations is algebraic. This generalizes results of V.G.~Safonov. In particular, we show that the lattice $l_{p_{\infty}}^{\tau}$ of all $\tau$-closed totally $p$-saturated formations is algebraic as well as the lattice $l_{\infty}^{\tau}$ of all $\tau$-closed totally saturated formations.
    Date of submission: 12 Aprel 2019 г.


  16. Rakhmelevich I.V. О многомерных детерминантных дифференциально-операторных уравнениях
    Status: reviewing
    Abstract.
    We consider a class of multi-dimensional determinant differential-operator equations, the left side of which represents a determinant with the elements containing a production of linear one-dimensional differential operators of arbitrary order. The right side of the equation depends on the unknown function and its first derivatives. There are separately investigated both homogeneous and inhomogeneous determinant differential-operator equations. The theorems on decreasing of dimension of equation are prooved. The theorem on interconnection between the solutions of initial equation and the solutions of some auxiliary linear equation is prooved for the homogeneous equation. Also there is obtained the solution of the homogeneous equation for the case when the linear differential operators containing in it, have proportional eigenvalues. There are received the solutions of travelling wave type, the solutions in the form of generalized monomials, and also the solutions expressed through the eigenfunctions of linear operators containing in the equation and the solutions expressed through the functions belong to the kernels of these operators.
    Date of submission: 22 Aprel 2019 г.


  17. Allahverdiev B.P., Tuna H. Existence of the solutions for a nonlinear singular $q$-Sturm-Liouville problems
    Status: reviewing
    Abstract.
    In this paper, we investigate a nonlinear $q$-Sturm-Liouville prob- lem on the semi in…nite interval in which the limit-circle case holds at in…nity for $q$-Sturm-Liouville expression. We show the existence and uniqueness of the solutions for this problem.
    Date of submission: 24 Aprel 2019 г.


  18. Bichegkuev M.S. Почти периодические на бесконечности решения интегро-дифференциальных уравнений с необратимым оператором при производной
    Status: reviewing
    Abstract.
    The spectral conditions of almost periodicity at infinity for bounded solutions of integro-differential equations with an irreversible operator at the derivative are obtained. The main results of the article are obtained on the basis of the use of the spectral theory of operator beams and methods of harmonic analysis. Applications to nonlinear differential equations are given.
    Date of submission: 30 Aprel 2019 г.


  19. AZARI Y., MESGARANI H., NIKAZAD T. SELF-REGULARIZATION PROPERTY OF LANDWEBER-TYPE ITERATIVE METHODS AND ITS APPLICATION FOR SOLVING ILL-POSED INTEGRAL EQUATIONS
    Status: reviewing
    Abstract.
    We consider Fredholm integral equation of the first kind that is intrinsically ill- posed inverse problem. Due to the ill-posedness of the problem, numerical solutions are very sensitive to perturbations and noises. These kinds of perturbations come from observation, measuring and rounding errors. Therefore, in practical applications our problem is always accompanied by noise. Hence the classical numerical methods, such as LU, QR and Cholesky factorizations, are failed to compute an appropriate solution. The regularization methods are well-known for solving these problems. We use Landweber-type iterative method and present its self-regularization property. Furthermore, we present a necessary and sufficient condition for the convergence analysis of the iterative method. The performance of the method is confirmed by four examples taken from Fredholm integral equation of the first kind. The efficiency, accuracy, and usefulness of the suggested method are illustrated by using numerical examples.
    Date of submission: 29 May 2019 г.


  20. AZARI Y., MESGARANI H., NIKAZAD T. A NEW ITERATIVE APPROACH FOR SOLVING ILL-POSED PROBLEMS
    Status: reviewing
    Abstract.
    Landweber-type methods are commonly applied to large-scale systems as an iter- ative method. However, there is no idea for initial iterate of the method and typically, it sets zero vector in the literature. In this paper, we use an inexpensive approach to compute initial iterate by combining the Golub-Kahan bidiagonalization and Tikhonov regularization method that improves the results of the component averaging (CAV) method and gives faster results. Furthermore, we present a necessary and sufficient condition for the convergence analysis of the iterative method. The new method easily applied to a variety of ill-posed problems affected by noise. Numerical experiments illustrate the performance of our iterative algorithms compared to the standard CAV method with fixed relaxation parameter and different strategy of relaxation parameter as well as modulus-based iterative methods for constrained Tikhonov regularization (MBI method).
    Date of submission: 29 May 2019 г.


  21. Rathod A. Uniqueness and Value Sharing of Meromomorphic Functions on Annuli
    Status: reviewing
    Abstract.
    In this paper, we study meromorphic functions that share only one value on annuli and prove the following results. Let f(z) and g(z) two non constant meromorphic functions on annli and For n ≥ 11, if f n f 0 and g n g 0 share the same nonzero and finite value a with the same multiplicities on an- nuli, then f ≡ dg or g = c 1 e cz and f = c 2 e −cz , where d is an (n + 1) th root of unity, c, c 1 and c 2 being constants.
    Date of submission: 04 June 2019 г.


  22. Rathod A. Uniqueness Theorems for Meromorphic Functions on Annuli
    Status: reviewing
    Abstract.
    In this paper, we discuss the uniqueness problems of meromorphic func- tions on annuli, we prove a general theorem on the uniqueness of meromorphic functions on annuli and from which an analog of Nevanlinna’s famous five-value theorem is proposed.
    Date of submission: 04 June 2019 г.


  23. Ishkin Kh.K., Marvanov R.I. Критерий эквивалентности двух асимптотических формул
    Status: reviewing
    Abstract.
    Исследуются условия эквивалентности двух асимптотических формул для произвольной неубывающей неограниченной последовательности $\{\lambda_n\}$. Получены две теоремы, доставляющие необходимое и достаточное условие на функцию $g$ или последовательность $\{f_n\}$, при котором одна из асимптотических формул $\lambda_n\sim f(n),\ n\to+\infty,$ или $N(\lambda)\sim g(\lambda), $ $ \lambda\to+\infty$, влечет другую.
    Date of submission: 20 June 2019 г.


  24. Fedotov A.I. On the asymptotic convergence of the polynomial collocation method for one class of singular integro-differential equations.
    Status: accepted в т.0 №0
    Abstract.
    For one class of singular integro-differential equations on the interval the polynomial collocation method is justified. For the justification the technic of reducing the polynomial collocation method to Galerkin method is used. This technic was first used by the author to justify the polynomial collocation method for the wide class of periodic singular integro-differential and pseudo-differential equations. Now for the first time this technic is used for the non-periodic case. It became possible due to the lemma, proved in this article by the author, that the interpolative Lagrange operator is bounded in the Sobolev spaces with the Chebyshev weight-function of the second kind. Just this result gives an opportunity to show that in non-periodic Sobolev spaces the poly-nomial collocation method converges to the exact solution with the same speed as Galerkin method.
    Date of submission: 24 June 2019 г.


  25. Shaikhullina P.A. Sectorial normalization of simplest germs of semihyperbolic maps in half-neighborhood
    Status: reviewing
    Abstract.
    There are considered the problem of analytical classification of the semi-hyperbolic maps by example of the simplest class of such germs on the plane (namely, the class of germs that are formally equivalent of 1-time shift of vector field $x^2\frac{\partial}{\partial x}+e^{\lambda}y\frac{\partial}{\partial y},~\lambda\in\mathbb{R}_+$). The theorem of sectorial normalization of such germs in semi-neighborhood in which is not exist a central manifold is proved. Also it's proved that the semi-formal normalizing map is asymptotic for the sectorial analytic normalizing map.
    Date of submission: 25 June 2019 г.


  26. Baishya K.K., BISWAS A., Das S. $\eta$-RICCI SOLITONS ON KENMOTSU MANIFOLDS ADMITTING GENERALIZED TANAKA WEBSTER-CONNECTION
    Status: reviewing
    Abstract.
    The object of the present paper is to study Ricci soli- tons with respect to generalized Tanaka-Webster connection [briefly (GT-W)] in Kenmotsu manifolds under some conditions and deter- mine the behaviour of Ricci soliton when the potential vector field V is pointwise collinear with the characteristic vector field ξ. Hav- ing found some incorrect results in ([1], [2], [3]), we attempt to rectify them.
    Date of submission: 16 July 2019 г.


  27. МАСТАЛИЕВ R.O. ОСОБЫЕ УПРАВЛЕНИЯ В СТОХАСТИЧЕСКИХ СИСТЕМАХ С ЗАПАЗДЫВАНИЕМ
    Status: reviewing
    Abstract.
    Рассматривается задача оптимального управления, в который состояние процессы определяется систем стохастических дифференциальных уравнений Ито с запаздывающим аргументом. На основе вариаций управления установлены новые необходимые условия оптимальности особых управлений в процессах, описываемых системой стохастических дифференциальных уравнений с запаздывающим аргументом.
    Date of submission: 17 July 2019 г.


  28. MANJULAMMA U., Nagaraja H.G. Almost Kenmotsu manifolds
    Status: reviewing
    Abstract.
    The object of this paper is to study almost Kenmotsu manifolds with characteristic vector field ξ belonging to (k,µ) 0 -nullity distribution. We prove that these manifolds reduce to Kenmotsu manifolds with scalar curvature -1. Further we establish the relations among the associated 1- forms and proved the conditons under which gradient Ricci almost soliton reduces to gradient Ricci soliton.
    Date of submission: 21 July 2019 г.


  29. Sethi A.K., Tripathy A. K. ON OSCILLATORY SECOND ORDER DIFFERENTIAL EQUATIONS WITH VARIABLE DELAYS
    Status: reviewing
    Abstract.
    In this work, we establish the sufficient conditions for oscillation of the second order neutral delay differential equations of the form: (r(t)((x(t) + p(t)x(τ(t))) 0 ) γ ) 0 + q(t)x α (σ(t)) + v(t)x β (η(t)) = 0 under the assumption that Z ∞ 0 ? 1 r(t) ? 1 γ dt < + ∞ for various ranges of p(t), where α, β and γ are the quotient of odd positive integers.
    Date of submission: 31 July 2019 г.


  30. Sahebi H.R. A Modified Nonlinear Midpoint Model for One-Parameter Family Mappings in Banach Spaces
    Status: reviewing
    Abstract.
    The main goal of this work is to introduce a new nonlinear midpoint model, based on iterative method, for finding a element of the set of fixed points of nonexpansive semigroup in smooth Banach spaces. The strong convergence of this model is proved under certain assumptions imposed on the iterative of parameters, which, in addition, is the unique solution of the variational inequality problem. Numerical simulations are also presented to verify the obtained results.
    Date of submission: 01 Avgust 2019 г.


  31. Sreelakshmi S., Thirupathi Reddy R., Venkateswarlu B. ON A CERTAIN SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY KOMATU INTEGRAL OPERATOR
    Status: reviewing
    Abstract.
    In the present paper, we have introduced a new subclass of analytic functions involving Komatu integral operator and obtained necessary and sufficient condition for this class. Further distortion theorem, linear combination and results on partial sums are investigated.
    Date of submission: 17 Avgust 2019 г.


  32. Chernov A.V. О СОХРАНЕНИИ ГЛОБАЛЬНОЙ РАЗРЕШИМОСТИ УПРАВЛЯЕМОГО ОПЕРАТОРНОГО УРАВНЕНИЯ ВТОРОГО РОДА.
    Status: reviewing
    Abstract.
    For a controlled evolutionary operator equation of the second kind in a Banach space we obtain sufficient conditions for the preservation of global solvability under small (with respect to the right-hand side increment with a fixed state) control variations. As examples we investigate the preservation of global solvability for the nonlinear Navier--Stokes system, the Benjamin--Bona--Mahony--Burgers equation, and also for certain strongly nonlinear pseudoparabolic equations.
    Date of submission: 27 Avgust 2019 г.


  33. Boukoucha R., Yahiaoui M. Coexistence of algebraic and non-algebraic limit cycles of a family of polynomial differential systems
    Status: reviewing
    Abstract.
    In this paper we introduce an explicit expression of invariant algebraic curves of a multi-parameter polynomial differential systems planar of degree seven, then we proved that these systems are integrable and we introduce an explicit expression of a first integral. Moreover, we determine sufficient conditions for these systems to possess two limit cycles : one of them is algebraic and the other one is showen to be non-algebraic, explicitly given. Concrete examples exhibiting the applicability of our result are introduced.
    Date of submission: 29 Avgust 2019 г.


  34. Ali S., Abdelwanis A.Y. SYMMETRIC BI-DERIVATIONS ON PARTIALLY ORDERED SETS
    Status: reviewing
    Abstract.
    Let P be a partially ordered set(poset). The objective of the present paper is to introduce and study the idea of symmetric bi-derivations of posets. Several characterization theorems involving symmetric bi-derivations are given. In particular, we prove that if d 1 and d 2 are two symmetric bi- derivations of P with traces φ 1 and φ 2 , then φ 1 ≤ φ 2 if and only if φ 2 (φ 1 (x)) = φ 1 (x) for all x ∈ P.
    Date of submission: 30 Avgust 2019 г.


  35. Iskhokov S.A., Rakhmonov B.A. On solvability and smoothness of a solution of the variational Dirichlet problem in the whole space associated with a noncoercive form
    Status: reviewing
    Abstract.
    We study the Variational Dirichlet problem for a class of higher order degenerate elliptic operators in the whole $n$-dimensional Euclidean space. A theorem on unique solvability of the problem is proved and under some additional condition on smoothness of coefficients and the right-hand side of the equation, differential properties of the solution are studied. A case when a solution of the variational Dirichlet problem stabilizes to a given polynomial at infinity. Formulation of the problem under consideration is connected with integro-differential sesquilinear form that may not satisfy the coercitivity condition.
    Date of submission: 02 September 2019 г.


  36. FAISAL M.I. GEOMETRIC CHARACTERISTICS OF THE CLASS RELATED WITH $p$-VALENT FUNCTIONS
    Status: reviewing
    Abstract.
    In this article, I introduce a class of p-valent analytic functions related to the simply connected convex set with the help of a differential operator defined in the open unit disk. I acquire some inclusion sequences and geometric characteristics of the class related with a simply connected convex set of p-valent analytic functions defined in the open unit disk.
    Date of submission: 16 September 2019 г.


  37. Najafzadeh Sh. Applying the H\"{o}lder inequality on univalent functions based on $q\!\op{--}$analogue of Salagean type operator
    Status: reviewing
    Abstract.
    $q\!\op{--}$analogue of Salagean type operator has been applied in this paper to investigate a new subclass of univalent functions defined in the open unit disk. We find estimates on the coefficients, convolution preserving property. Moreover, we point out coefficient bounds and convolution preserving property. The H\"{o}lder inequality is also indicated.
    Date of submission: 22 September 2019 г.


  38. Truhlyaeva I.V. Estimate of a polynomial characteristic of a multidimensional domain
    Status: reviewing
    Abstract.
    In this paper we consider the polynomial approximate solutions of the Dirichlet problem for minimal surface equation. It is shown that under certain conditions on the geometric structure of the domain the absolute values of the gradients of the solutions are bounded as the degree of these polynomials increases. The obtained properties imply the uniform convergence of approximate solutions to the exact solution of the minimal surface equation.
    Date of submission: 23 September 2019 г.


  39. Falaleev M.V. Fundamental Operator-functions of Integro-Differential Operators Under Spectral or Polynomial Constraints
    Status: reviewing
    Abstract.
    This paper investigates the Cauchy problem for a degenerate high order integro-differential equation in Banach spaces. For the equations under study, the corresponding fundamental operator functions are constructed, with the help of which the only generalized solution of the original Cauchy problem in the class of distributions with a left-bounded carrier is restored. The analysis of the resulting generalized solution allows us to investigate the solvability problem in the classical sense. The fundamental operator-function is constructed in terms of the theory of semigroups of operators with kernels. Abstract results are illustrated by examples of initial-boundary value problems of viscoelasticity theory.
    Date of submission: 25 September 2019 г.