One-parametric family of positive solutions for a class of nonlinear discrete Hammerstein-Volterra equations

Abstract

. In the present work we study a class of of nonlinear discrete Hammerstein-Volterra equations in a post-critical case. We prove the existence of a one-parametric family of positive solutions in space 𝑙 1 . We describe the set of parameters and establish the monotonic dependence of each solution both in a parameter and a corresponding index.