Article
Ufa Mathematical Journal
Volume 13, Number 1, pp. 17-30
Nonlinear convolution type integral equations in complex spaces
Askhabov S.N.
DOI:10.13108/2021-13-1-17
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We study various classes of nonlinear convolution type integral equations appearing in the theory of feedback systems, models of population genetics and other. By the method of monotone in the Browder-Minti operators we prove global theorems on existence, uniqueness and estimates for the solutions to the considered equations in complex Lebesgue spaces $L_p(\mathds{R})$ under rather simple restrictions for the nonlinearities. Subject to the considered class of equations, weassume that either $p\in (1,2]$ or $p\in [2,\infty)$. The conditions imposed on nonlinearities are necessary and sufficient to ensure that the generated superposition operators act from the space $L_p(\mathds{R})$, $1