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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN // Archive

Trudy Inst. Mat. i Mekh. UrO RAN, 2023 Volume 29, Number 1, Pages 202–218 (Mi timm1988)

This article is cited in 2 papers

Existence and uniqueness theorems for one system of integral equations with two nonlinearities

Kh. A. Khachatryanab, H. S. Petrosyancb, M. H. Avetisyanc

a Yerevan State University
b Lomonosov Moscow State University
c National Agrarian University of Armenia

Abstract: We consider a system of integral equations on the positive semiaxis with two monotone nonlinearities. With various particular representations of matrix kernels and nonlinearities, this system arises in many branches of mathematical physics. A constructive existence theorem for a non-negative, non-trivial and bounded solution is proved. We also study the asymptotic behavior of the solution at infinity. Under additional restrictions on the nonlinearities and matrix kernels, a uniqueness theorem for a solution, in a certain class of bounded vector functions, is proved. At the end, specific examples of matrix kernels and nonlinearities are given.

Keywords: matrix kernel, nonlinearity, bounded solution, monotonicity, convergence, limit relation.

UDC: 517.968.48

MSC: 45G15, 35B27, 35B40

Received: 09.01.2023
Revised: 23.01.2023
Accepted: 30.01.2023

DOI: 10.21538/0134-4889-2023-29-1-202-218



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