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Research Article | Open Access

Least energy sign-changing solution for a fractional p-Laplacian problem with exponential critical growth

Kun Cheng1( ), Wentao Huang2, Li Wang2
School of Information Engineering, Jingdezhen Ceramic University, Jingdezhen 333403, China
College of Science, East China Jiaotong University, Nanchang 330013, China
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Abstract

In this paper, we consider the following fractional p-Laplacian equation involving Trudinger-Moser nonlinearity:

(−Δ)N/ssu+V(x)|u|Ns−2u=f(u)inRN,

where s∈(0,1),2<Ns=p. The nonlinear function f has exponential critical growth, and potential V is a continuous function. By using the constrained variational methods, quantitative Deformation Lemma and Brouwer degree theory, we prove the existence of least energy sign-changing solutions.

Keywords

sign-changing solutionfractional p-Laplacianexponential critical growth
CLC number: 35J60, 35J92, 35R11

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AIMS Mathematics
Volume 7 Issue 12,
December 2022
Pages 20797-20822
DOI: 10.3934/math.20221140

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Cite this article:
Cheng K, Huang W, Wang L. Least energy sign-changing solution for a fractional p-Laplacian problem with exponential critical growth. AIMS Mathematics, 2022, 7(12): 20797-20822. https://doi.org/10.3934/math.20221140

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Received: 21 August 2022
Revised: 14 September 2022
Accepted: 21 September 2022
Published: 15 December 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)