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

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