Work

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

Year: 2025

Type: article

Abstract: The purpose of this paper is to examine a class of elliptic problems that involve negative potentials $ a\in L^{\frac{N}{2} }(\Omega) $ and critical nonlinearities. To discuss this, the well-known eigenvalue problem $ -\Delta- a $ is considered. Under some mild assumptions, an existence result is obtained, which extends the existing results to the critical case.

Source: AIMS Mathematics

DOI: 10.3934/math.2025336

Authors: Ye Xue, Yongzhen Ge, Yunlan Wei

Institutions: Changzhou University, Linyi University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province