Work

Existence and Concentration of Solutions for Discontinuous Elliptic Problems With Critical Growth

Year: 2025

Type: article

Abstract: This paper concerns the following elliptical problem with discontinuous nonlinearity $\left\{\begin{array}{l}-\epsilon^2 \Delta u+V(x) u=f(u)+|u|^{2^*-2} u, \quad x \in \mathbb{R}^N, \\u>0,\end{array}\right.$ where N ≥ 3, ε > 0 and f(u) is a discontinuous function. We obtain the existence and concentration results of this problem. Our results generalize some recent results on this kind of problems. In order to obtain these results, a suitable truncation, concentration compactness principle, new analytic technique and variational method are used.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240241

Author: Ziqing Yuan

Institution: Shaoyang University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: National Natural Science Foundation of China

Award: G606261409