Existence and multiplicity of nontrivial solutions for nonlinear fractional differential systems with p‐Laplacian via critical point theory. (21st February 2018)

• Record Type: Journal Article
• Authors: Li, Dongping; Chen, Fangqi; An, Yukun
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 8(2018)
• Page Start: 3197
• Page End: 3212
• Publication Date: 2018-02-21
• Subjects: p‐Laplacian operator -- critical point theorem -- boundary value problem -- fractional differential systems; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4810
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, the existence and multiplicity of nontrivial solutions are obtained for nonlinear fractional differential systems with p ‐Laplacian by combining the properties of fractional calculus with critical point theory. Firstly, we present a result that a class of p ‐Laplacian fractional differential systems exists infinitely many solutions under the famous Ambrosetti‐Rabinowitz condition. Then, a criterion is given to guarantee that the fractional systems exist at least 1 nontrivial solution without satisfying Ambrosetti‐Rabinowitz condition. Our results generalize some existing results in the literature.