A system of nonlinear integral equations with a noncompact monotone Hammerstein type matrix integral operator is studied on the positive half-line. For specific representations of matrix kernels and nonlinearities involved in the system, the class of vector nonlinear integral equations under consideration has applications in various areas of mathematical physics. In particular, such systems arise in the theory of radiative transfer in inhomogeneous media, in the kinetic theory of gases, and in mathematical biology. The existence of a nontrivial componentwise nonnegative and bounded solution is proved. In one important particular case, the integral asymptotic behavior of the constructed solution is also studied. At the end of the paper, specific examples of nonlinearities and matrix kernels that satisfy the conditions of the formulated theorems are given.
Keywords: monotonicity, bounded solution, iterations, convexity, nonlinearity, convergence
Received March 2, 2022
Revised March 30, 2022
Accepted April 11, 2021
Funding Agency: This work was supported by the Science Committee of the Republic of Armenia (project no. 21T-1A047).
Khachatur Aghavardovich Khachatryan, Dr. Phys.-Math. Sci., Prof., Yerevan State University, 0025 Yerevan, Republic of Armenia, e-mail: Khach82@rambler.ru, khachatur.khachatryan@ysu.am
Haykanush Samvelovna Petrosyan, Cand. Sci. (Phys.-Math.), Armenian National Agrarian University, 0009, Yerevan, Republic of Armenia, e-mail: Haykuhi25@mail.ru
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Cite this article as: Kh.A. Khachatryan, H.S. Petrosyan. On the solvability of a system of nonlinear integral equations with a monotone Hammerstein type operator, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2022, vol. 28, no. 2, pp. 201–214.
