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IMCS/Publications/BASM/Issues/BASM n.2 (78), 2015/

Solvability of a nonlinear integral equation arising in kinetic theory

Authors: A. Kh. Khachatryan, Kh. A. Khachatryan

Abstract

In the paper the question of solvability of an Urysohn type nonlinear integral equation arising in kinetic theory of gases has been studied. We prove the existence of a positive and bounded solution and also suggest an approach for the construction of a solution. We also show that there is a qualitative difference between solutions in the linear and nonlinear cases. In the nonlinear case the solution is a positive and bounded function, while the corresponding linear equation has an alternating solution, which possesses linear growth at infinity.

Institute of Mathematics
of National Academy of Sciences of Armenia
E-mail: ,

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