Approximating solutions of nonlinear PBVPs of second-order differential equations via hybrid fixed point theory

Abstract

In this article we prove the existence and approximations of solutions of periodic boundary-value problems of second-order ordinary nonlinear hybrid differential equations. We rely our results on Dhage iteration principle or method embodied in a recent hybrid fixed point theorem of Dhage (2014) in partially ordered normed linear spaces. Our resutls are proved under weaker continuity and Lipschitz conditions. An example illustrates the theory developed in this article.

Keywords

• Hybrid differential equation
• periodic boundary value problems
• Dhage iteration method
• hybrid fixed point theorem
• approximate solution