Kh. A. Khachatryan, H. S. Petrosyan, “On alternating and bounded solutions of one class of integral equations on the entire axis with monotonic nonlinearity”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2020, Volume 24, Number 4,Pages <nobr>644

Differential Equations and Mathematical Physics

On alternating and bounded solutions of one class of integral equations on the entire axis with monotonic nonlinearity

Kh. A. Khachatryan^abc, H. S. Petrosyan^ad

^a Lomonosov Moscow State University, Moscow, 119992, Russian Federation
^b Institute of Mathematics, National Academy of Sciences of Armenia, Yerevan, 0019, Armenia
^c Yerevan State University, Yerevan, 0025, Armenia
^d National Agrarian University of Armenia, Yerevan, 0009, Armenia

Abstract: The paper is devoted to the study of the existence and analysis of the qualitative properties of solutions for one class of integral equations with monotonic nonlinearity on the entire line. The indicated class of equations arises in the kinetic theory of gases. The constructive theorems of the existence of bounded solutions are proved, and certain qualitative properties of the constructed solutions are studied. At the end of the paper, specific applied examples of these equations are given.

Keywords: monotonicity, nonlinearity, kernel, convexity, limited solution.

UDC: 517.968.74

MSC: 45G05

Received: June 10, 2020
Revised: October 16, 2020
Accepted: November 16, 2020
First online: December 19, 2020

DOI: 10.14498/vsgtu1790