Existence of solutions for nonlinear impulsive qk -difference equations with first-order qk -derivatives

Abstract

In this paper, we study the nonlinear second-order impulsive q k -difference equations with Sturm-Liouville type, in which nonlinear team and impulsive teams are dependent on first-order q k -derivatives. We obtain the existence and uniqueness results of solutions for the problem by Banach's contraction mapping principle and Schaefer's fixed point theorems. Finally, we give two examples to demonstrate the use of the main results. c 2016 All rights reserved.Keywords: q k -derivative, q k -integral, impulsive q k -difference equation, boundary value problem, fixed point theorem. 2010 MSC: 39A13, 34B15, 34B37, 81Q99.