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Research Article | Open Access

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

Zhiwei Lv1, Jiafa Xu2( ), Donal O'Regan3
School of Sciences and Arts, Suqian University, Suqian 223800, China
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
School of Mathematical and Statistical Sciences, National University of Ireland, Galway, Ireland
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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.

Keywords

fractional p-Laplacian equationweak solutiontopological degreefountain theorem(p − 1)-asymptotically linearLandesman-Lazer type condition
CLC number: 35A15, 35R11, 47A10

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 13258-13270
DOI: 10.3934/math.2022731

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Cite this article:
Lv Z, Xu J, O'Regan D. Solvability for a fractional p-Laplacian equation in a bounded domain. AIMS Mathematics, 2022, 7(7): 13258-13270. https://doi.org/10.3934/math.2022731

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Received: 08 March 2022
Revised: 02 May 2022
Accepted: 06 May 2022
Published: 15 July 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)