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Existence and multiplicity of nontrivial solutions for nonlinear fractional differential systems with p ‐Laplacian via critical point theory
Author(s) -
Li Dongping,
Chen Fangqi,
An Yukun
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4810
Subject(s) - mathematics , multiplicity (mathematics) , nonlinear system , fractional laplacian , fractional calculus , laplace operator , p laplacian , critical point (mathematics) , class (philosophy) , mathematical analysis , pure mathematics , boundary value problem , physics , quantum mechanics , artificial intelligence , computer science
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.