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EXISTENCE RESULTS FOR ANTI-PERIODIC BOUNDARY VALUE PROBLEMS OF NONLINEAR SECOND-ORDER IMPULSIVE qk-DIFFERENCE EQUATIONS
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 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;
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 Abstract
Based on the notion of -derivative introduced by the authors in [17], we prove in this paper existence and uniqueness results for nonlinear second-order impulsive -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
-derivative;-integral;impulsive -difference equation;existence;uniqueness;anti-periodic boundary conditions;fixed point theorems;
 Language
English
 Cited by
 References
1.
B. Ahmad, Boundary-value problems for nonlinear third-order q-difference equations, Electron. J. Differential Equations 2011 (2011), no. 94, 1-7.

2.
B. Ahmad, A. Alsaedi, and S. K. Ntouyas, A study of second-order q-difference equations with boundary conditions, Adv. Difference Equ. 2012 (2012), 35, 10 pp. crossref(new window)

3.
B. Ahmad and J. J. Nieto, On nonlocal boundary value problems of nonlinear q-difference equations, Adv. Difference Equ. 2012 (2012), 81, 10 pp. crossref(new window)

4.
B. Ahmad and S. K. Ntouyas, Boundary value problems for q-difference inclusions, Abstr. Appl. Anal. 2011 (2011), ID 292860, 15 pages.

5.
B. Ahmad, S. K. Ntouyas, and I. K. Purnaras, Existence results for nonlinear q-difference equations with nonlocal boundary conditions, Comm. Appl. Nonlinear Anal. 19 (2012), no. 3, 59-72.

6.
G. Bangerezako, Variational q-calculus, J. Math. Anal. Appl. 289 (2004), no. 2, 650-665. crossref(new window)

7.
M. Benchohra, J. Henderson, and S. K. Ntouyas, Impulsive Differential Equations and Inclusions, vol. 2, Hindawi Publishing Corporation, New York, 2006.

8.
M. Bohner and G. Sh. Guseinov, The h-Laplace and q-Laplace transforms, J. Math. Anal. Appl. 365 (2010), no. 1, 75-92. crossref(new window)

9.
A. Dobrogowska and A. Odzijewicz, Second order q-difference equations solvable by factorization method, J. Comput. Appl. Math. 193 (2006), no. 1, 319-346. crossref(new window)

10.
M. El-Shahed and H. A. Hassan, Positive solutions of q-difference equation, Proc. Amer. Math. Soc. 138 (2010), no. 5, 1733-1738.

11.
G. Gasper and M. Rahman, Some systems of multivariable orthogonal q-Racah polyno-mials, Ramanujan J. 13 (2007), no. 1-3, 389-405. crossref(new window)

12.
M. E. H. Ismail and P. Simeonov, q-difference operators for orthogonal polynomials, J. Comput. Appl. Math. 233 (2009), no. 3, 749-761. crossref(new window)

13.
V. Kac and P. Cheung, Quantum Calculus, Springer, New York, 2002.

14.
M. A. Krasnoselskii, Two remarks on the method of successive approximations, Uspekhi Mat. Nauk 10 (1955), no. 1, 123-127.

15.
V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore-London, 1989.

16.
A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.

17.
J. Tariboon and S. K. Ntouyas, Quantum calculus on finite intervals and applications to impulsive difference equations, Adv. Difference Equ. 2013 (2013), 282, 19 pp. crossref(new window)

18.
C. Yu and J. Wang, Existence of solutions for nonlinear second-order q-difference equa-tions with first-order q-derivatives, Adv. Difference Equ. 2013 (2013), 124, 11 pp. crossref(new window)

19.
W. Zhou and H. Liu, Existence solutions for boundary value problem of nonlinear frac-tional q-difference equations, Adv. Difference Equ. 2013 (2013), 113, 12 pp. crossref(new window)