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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)
  • Received : 2014.01.14
  • Published : 2016.03.31

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

Acknowledgement

Supported by : King Mongkut's University of Technology North Bangkok

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