Solvability for a fractional $ p $-Laplacian equation in a bounded domain

Zhiwei Lv; Jiafa Xu; Donal O'Regan; Zhiwei Lv; Jiafa Xu; Donal O'Regan

doi:10.3934/math.2022731

AIMS Mathematics

2022, Volume 7, Issue 7: 13258-13270. doi: 10.3934/math.2022731

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Solvability for a fractional $ p $-Laplacian equation in a bounded domain

1.
School of Sciences and Arts, Suqian University, Suqian 223800, China
2.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
3.
School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland

Received: 08 March 2022 Revised: 02 May 2022 Accepted: 06 May 2022 Published: 13 May 2022
MSC : 35A15, 35R11, 47A10

In this paper we use the topological degree and the fountain theorem to study the existence of weak solutions for a fractional $ p $-Laplacian equation in a bounded domain. For the nonlinearity $ f $, we consider two situations: (1) the non-resonance case where $ f $ is $ (p-1) $-asymptotically linear at infinity; (2) the resonance case where $ f $ satisfies the Landesman-Lazer type condition.
- fractional $ p $-Laplacian equation,
- weak solution,
- topological degree,
- fountain theorem,
- $ (p-1) $-asymptotically linear,
- Landesman-Lazer type condition
Citation: Zhiwei Lv, Jiafa Xu, Donal O'Regan. Solvability for a fractional $ p $-Laplacian equation in a bounded domain[J]. AIMS Mathematics, 2022, 7(7): 13258-13270. doi: 10.3934/math.2022731

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Abstract

In this paper we use the topological degree and the fountain theorem to study the existence of weak solutions for a fractional $ p $-Laplacian equation in a bounded domain. For the nonlinearity $ f $, we consider two situations: (1) the non-resonance case where $ f $ is $ (p-1) $-asymptotically linear at infinity; (2) the resonance case where $ f $ satisfies the Landesman-Lazer type condition.

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