Dirichlet problems of fractional $ p $-Laplacian equation with impulsive effects

Xiaolin Fan; Tingting Xue; Yongsheng Jiang; Xiaolin Fan; Tingting Xue; Yongsheng Jiang

doi:10.3934/mbe.2023236

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 5094-5116. doi: 10.3934/mbe.2023236

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Dirichlet problems of fractional $ p $-Laplacian equation with impulsive effects

School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China

Academic Editor: Feliz Minhós

Received: 27 October 2022 Revised: 22 December 2022 Accepted: 26 December 2022 Published: 06 January 2023

The purpose of the article is to investigate Dirichlet boundary-value problems of the fractional $ p $-Laplacian equation with impulsive effects. By using the Nehari manifold method, mountain pass theorem and three critical points theorem, some new results are achieved under more general growth conditions. In addition, this paper weakens the commonly used $ p $-suplinear and $ p $-sublinear growth conditions.
- fractional Dirichlet problem,
- $ p $-Laplacian operator,
- impulsive effect,
- ground state solution,
- weak solution
Citation: Xiaolin Fan, Tingting Xue, Yongsheng Jiang. Dirichlet problems of fractional $ p $-Laplacian equation with impulsive effects[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 5094-5116. doi: 10.3934/mbe.2023236

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Abstract

The purpose of the article is to investigate Dirichlet boundary-value problems of the fractional $ p $-Laplacian equation with impulsive effects. By using the Nehari manifold method, mountain pass theorem and three critical points theorem, some new results are achieved under more general growth conditions. In addition, this paper weakens the commonly used $ p $-suplinear and $ p $-sublinear growth conditions.

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