Article
Ufa Mathematical Journal
Volume 9, Number 1, pp. 75-88
Analogue of Bohl theorem for a class of linear partial differential
equations
Mukhamadiev E.M., Naimov A.N., Sattorov A.H.
DOI:10.13108/2017-9-1-75
Download PDF
Article on MathNetAbstact
We study the issue on the existence
and uniqueness of a solution bounded in the entire space for a class of higher order linear partial differential equations. We prove the theorem on the necessary and sufficient condition for
the existence
and uniqueness of a bounded solution for a studied class of equations. This theorem is an analogue of the Bohl theorem known in the theory of ordinary differential equations. In a partial case the unique solvability conditions are expressed in terms of the coefficients of the equation and we provide the integral representation for the bounded solution.