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Research Article | Open Access

The existence of a nontrivial solution to an elliptic equation with critical Sobolev exponent and a general potential well

Ye Xue1, Yongzhen Ge1( ), Yunlan Wei2
Department of Mathematics, Changzhou University, Changzhou 213164, China
School of Mathematics and Statistics, Linyi University, Linyi 276000, China
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Abstract

The purpose of this paper is to examine a class of elliptic problems that involve negative potentials a ∈ L N 2 ( Ω ) and critical nonlinearities. To discuss this, the well-known eigenvalue problem − Δ − a is considered. Under some mild assumptions, an existence result is obtained, which extends the existing results to the critical case.

Keywords

elliptic equationexistencegeneral potentialcritical Sobolev exponent
CLC number: 35A15, 35J60

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 7339-7354
DOI: 10.3934/math.2025336

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Cite this article:
Xue Y, Ge Y, Wei Y. The existence of a nontrivial solution to an elliptic equation with critical Sobolev exponent and a general potential well. AIMS Mathematics, 2025, 10(3): 7339-7354. https://doi.org/10.3934/math.2025336

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Received: 17 January 2025
Revised: 14 March 2025
Accepted: 21 March 2025
Published: 15 March 2025
©2025 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)