Mathematical Methods in the Applied Sciences

RESEARCH ARTICLE

Existence and multiplicity of nontrivial solutions for nonlinear fractional differential systems with p-Laplacian via critical point theory

Dongping Li

orcid.org/0000-0002-4946-7627

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China

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Fangqi Chen,

Corresponding Author

Fangqi Chen

[email protected]

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, People's Republic of China

Correspondence

Fangqi Chen and Yukun An, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China.

Email: [email protected]; [email protected]

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Yukun An,

Corresponding Author

Yukun An

[email protected]

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China

Correspondence

Fangqi Chen and Yukun An, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China.

Email: [email protected]; [email protected]

Search for more papers by this author

Dongping Li,

Dongping Li

orcid.org/0000-0002-4946-7627

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China

Search for more papers by this author

Fangqi Chen,

Corresponding Author

Fangqi Chen

[email protected]

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, People's Republic of China

Correspondence

Fangqi Chen and Yukun An, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China.

Email: [email protected]; [email protected]

Search for more papers by this author

Yukun An,

Corresponding Author

Yukun An

[email protected]

Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China

Correspondence

Fangqi Chen and Yukun An, Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, People's Republic of China.

Email: [email protected]; [email protected]

Search for more papers by this author

First published: 21 February 2018

https://doi.org/10.1002/mma.4810

Citations: 27

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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.

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Volume41, Issue8

30 May 2018

Pages 3197-3212

Existence and multiplicity of nontrivial solutions for nonlinear fractional differential systems with p-Laplacian via critical point theory

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Existence and multiplicity of nontrivial solutions for nonlinear fractional differential systems with p-Laplacian via critical point theory

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