Positive solutions to a class of q-fractional difference boundary value problems with \(\phi\)-Laplacian operator

Volume 9, Issue 6, pp 3802--3807 http://dx.doi.org/10.22436/jnsa.009.06.29

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Authors

Jidong Zhao - Department of Foundation, Shandong Yingcai University, Jinan, Shandong 250104, P. R. China.

Abstract

By virtue of the upper and lower solutions method, as well as the Schauder fixed point theorem, the existence of positive solutions to a class of q-fractional difference boundary value problems with \(\phi\)-Laplacian operator is investigated. The conclusions here extend existing results.

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Keywords

• Fractional q-difference
• \(\phi\)-Laplacian operator
• upper and lower solutions method
• Schauder fixed point theorem
• positive solution.

MSC

•  34A08
•  34B18
•  39A13

References

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• [2] R. A. C. Ferreira, Positive solutions for a class of boundary value problems with q-fractional differences, Comput. Math. Appl., 61 (2011), 367-373.


• [3] V. Kac, P. Cheungşel, Quantum Calculus, Springer Press, New York (2002)


• [4] F. Miao, S. Liang, Uniqueness of positive solutions for fractional difference boundary-value problems with p- Laplacian operator, Electron. J. Differ. Equ., 2013 (2013), 11 pages.


• [5] W. Yang, Positive solution for q-fractional difference boundary value problems with \(\phi\)-Laplacian operator, Bull. Malays. Math. Sci. Soc., 36 (2013), 1195-1203.


• [6] L. Yang, H. Chen, L. P. Luo, Z. G. Luo, Successive iteration and positive solutions for boundary value problem of nonlinear q-fractional difference equation, J. Appl. Math. Comput, 42 (2013), 89-102.