One-parameter family of integrable solutions of a system of nonlinear integral equations of the Hammerstein–Volterra type in the supercritical case

Abstract

We study a system of nonlinear integral equations of the Hammerstein–Volterra type on a half-line in the supercritical case. We show that this system has a one-parameter family of positive integrable bounded solutions. We describe the structure of each solution in this family. The monotone dependence of the solutions on the parameter is proved.