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

Zhiwei Lv; Jiafa Xu; Donal O’regan

doi:10.3934/math.2022731

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

Zhiwei Lv, Jiafa Xu, Donal O’regan

Mathematics

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	13258-13270
Number of pages	13
Journal	AIMS Mathematics
Volume	7
Issue number	7
DOIs	https://doi.org/10.3934/math.2022731
Publication status	Published - 2022

Keywords

(p − 1)-asymptotically linear
fountain theorem
fractional p-Laplacian equation
Landesman-Lazer type condition
topological degree
weak solution

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10.3934/math.2022731

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title = "Solvability for a fractional p-Laplacian equation in a bounded domain",

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 = "(p − 1)-asymptotically linear, fountain theorem, fractional p-Laplacian equation, Landesman-Lazer type condition, topological degree, weak solution",

author = "Zhiwei Lv and Jiafa Xu and Donal O{\textquoteright}regan",

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AU - Lv, Zhiwei

AU - Xu, Jiafa

AU - O’regan, Donal

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - (p − 1)-asymptotically linear

KW - fountain theorem

KW - fractional p-Laplacian equation

KW - Landesman-Lazer type condition

KW - topological degree

KW - weak solution

UR - https://www.scopus.com/pages/publications/85131621152

U2 - 10.3934/math.2022731

DO - 10.3934/math.2022731

M3 - Article

AN - SCOPUS:85131621152

SN - 2473-6988

VL - 7

SP - 13258

EP - 13270

JO - AIMS Mathematics

JF - AIMS Mathematics

IS - 7

ER -

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

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Keywords

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