Constant-Sign Solutions of a System of Urysohn Integral Equations

Abstract

We consider the following system of Urysohn integral equations By using fixed point theorems and fixed point index theory, criteria are established for the existence of single, double and multiple solutions of the system that are of constant signs, i.e., for each 1 ≤ i ≤ n, u i (t) ≥ 0 or u i (t) ≤ 0 for t ∈ [0,1]. We also consider the eigenvalue problem where criteria are derived such that for λ in some interval, the existence of a constant-sign solution is guaranteed.