Sequential Derivatives of Nonlinear q-Difference Equations with Three-Point q-Integral Boundary Conditions

Abstract

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinear $q$-difference equations with three-point $q$-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.