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

Title & Authors
EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE qk-DIFFERENCE EQUATIONS
Ntouyas, Sotiris K.; Tariboon, Jessada; Thiramanus, Phollakrit;

Abstract
Based on the notion of $\small{q_k}$-derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive $\small{q_k}$-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
$\small{q_k}$-derivative;$\small{q_k}$-integral;impulsive $\small{q_k}$-difference equation;existence;uniqueness;anti-periodic boundary conditions;fixed point theorems;
Language
English
Cited by
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