Nonlocal boundary value problems for second-order nonlinear Hahn integro-difference equations with integral boundary conditions

Abstract

Abstract In this paper, we study a boundary value problem for second-order nonlinear Hahn integro-difference equations with nonlocal integral boundary conditions. Our problem contains two Hahn difference operators and a Hahn integral. The existence and uniqueness of solutions is obtained by using the Banach fixed point theorem, and the existence of at least one solution is established by using the Leray-Schauder nonlinear alternative and Krasnoselskii’s fixed point theorem. Illustrative examples are also presented to show the applicability of our results.

Keywords

• Hahn difference equations
• boundary value problems
• existence
• uniqueness
• fixed point theorems