Extremal solutions for singular fractional p -Laplacian differential equations with nonlinear boundary conditions

Advances in Difference Equations

Youzheng Ding¹  Jian Yang²  Xiaoyan Zhang³ 

[1] Department of Mathematics, Shandong Jianzhu University, Jinan, China;School of Mathematical Science, University of Jinan, Jinan, China;School of Mathematics, Shandong University, Jinan, China

关键词: fractional differential equation;    p-Laplacian operator;    nonlinear boundary condition;    upper and lower solutions;    extremal solution;    26A33;    34B15;    34A08;   

DOI  :  10.1186/s13662-016-0926-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we establish the existence and uniqueness of extremal solutions for nonlinear boundary value problems of a singular fractional p-Laplacian differential equation involving Riemann-Liouville derivatives. Our results are obtained by constructing monotone iterative sequences of upper and lower solutions and applying the comparison result. At last, we present an example to illustrate the results. The compactness of sequences is proved in the Appendix.

【 授权许可】

CC BY