Positive almost periodic solutions to integral equations with superlinear perturbations via a new fixed point theorem in cones

Abstract

In this article, we establish a new fixed point theorem for nonlinear operators with superlinear perturbations in partially ordered Banach spaces, Then we use the fixed point theorem to prove the existence of positive almost periodic solutions to some integral equations with superlinear perturbations. Also, a concrete example is given to illustrate our results.

Keywords

• Almost periodic
• delay integral equation
• positive solution
• superlinear perturbation