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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.

Existence results for anti-periodic boundary value problems of nonlinear second-order impulsive $q_k$-difference equations

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

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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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