Existence and subharmonicity of solutions for nonsmooth $ p $-Laplacian systems

Yan Ning; Daowei Lu; Anmin Mao; Yan Ning; Daowei Lu; Anmin Mao

doi:10.3934/math.2021636

AIMS Mathematics

2021, Volume 6, Issue 10: 10947-10963. doi: 10.3934/math.2021636

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Existence and subharmonicity of solutions for nonsmooth $ p $-Laplacian systems

1.
School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, China
2.
Department of Mathematics, Jining University, Qufu, Shandong 273155, China

Received: 01 April 2021 Accepted: 11 July 2021 Published: 29 July 2021
MSC : 37J12, 37J46

In this paper we study nonlinear periodic systems driven by the vectorial $ p $-Laplacian with a nonsmooth locally Lipschitz potential function. Using variational methods based on nonsmooth critical point theory, some existence of periodic and subharmonic results are obtained, which improve and extend related works.
- $ p $-Laplacian,
- locally Lipschitz continuous,
- nonsmooth saddle point theorem,
- subharmonic solution,
- periodic solution
Citation: Yan Ning, Daowei Lu, Anmin Mao. Existence and subharmonicity of solutions for nonsmooth $ p $-Laplacian systems[J]. AIMS Mathematics, 2021, 6(10): 10947-10963. doi: 10.3934/math.2021636

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Abstract

In this paper we study nonlinear periodic systems driven by the vectorial $ p $-Laplacian with a nonsmooth locally Lipschitz potential function. Using variational methods based on nonsmooth critical point theory, some existence of periodic and subharmonic results are obtained, which improve and extend related works.

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