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http://dx.doi.org/10.4134/BKMS.2016.53.2.335

EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE qk-DIFFERENCE EQUATIONS  

Ntouyas, Sotiris K. (Department of Mathematics, University of Ioannina, Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University)
Tariboon, Jessada (Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok)
Thiramanus, Phollakrit (Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.2, 2016 , pp. 335-350 More about this Journal
Abstract
Based on the notion of $q_k$-derivative introduced by the authors in [17], 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;
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