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

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.