Bull. Korean Math. Soc. 2016; 53(2): 335-350
Printed March 31, 2016
https://doi.org/10.4134/BKMS.2016.53.2.335
Copyright © The Korean Mathematical Society.
Sotiris K. Ntouyas, Jessada Tariboon, and Phollakrit Thiramanus
University of Ioannina, King Mongkut's University of Technology North Bangkok, King Mongkut's University of Technology North Bangkok
Based on the notion of $q_k$-derivative introduced by the authors in \cite{TN}, we prove in this paper existence and uniqueness results for nonlinear second-order impulsive $q_k$-difference equations with anti-periodic boundary conditions. Two results are obtained by applying Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. Some examples are presented to illustrate the results.
Keywords: $q_k$-derivative, $q_k$-integral, impulsive $q_k$-difference equation, existence, uniqueness, anti-periodic boundary conditions, fixed point theorems
MSC numbers: 34B37, 39A13, 34A37
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