Solutions for a nonlinear fractional boundary value problem with sign-changing Greens function

Volume 8, Issue 5, pp 650--659 http://dx.doi.org/10.22436/jnsa.008.05.17

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Authors

Youzheng Ding - Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong, 250101, China. Zhongli Wei - Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong, 250101, China. Qingli Zhao - Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong, 250101, China.

Abstract

This paper considers the existence, uniqueness and non-existence of solution for a quasi-linear fractional boundary value problems with sign-changing Green’s function. Under certain growth conditions on the nonlinear term, we employ the Leray-Schauder alternative fixed point theorem to obtain an existence result of nontrivial solution and use the Banach contraction mapping principle to obtain a uniqueness result. Moreover, the existence result of positive solutions is obtained when the nonlinear term is also allowed to change sign.

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Keywords

• Fractional boundary value problem
• fixed point theorem
• sign-changing Green’s function
• positive solution
• existence.

MSC

•  34B15
•  34B18

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