Work

Existence of positive solutions to anisotropic elliptic equations in bounded domain of $ \mathbb{R}^{N} $

Year: 2025

Type: article

Abstract: In this paper, an anisotropic elliptic equation in a bounded domain of $ \mathbb{R}^{N} $ is considered. Assume that the nonlinearity of the equation has exponential growth or critical growth. It is proved that this equation has a nontrivial positive weak solution by the mountain-pass theorem. Furthermore, it is shown that there are two distinct positive solutions to a perturbation of the equation by applying the anisotropic Moser-Trudinger inequality, mountain-pass theorem, and Ekeland's variational principle.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2025084

Authors: Rulong Xie, Lei Yang

Institutions: Anhui Normal University, Chaohu 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

Awards: G222581545, G4371696611, Gross-Pitaevskii方程及Ermakov系统相关问题的研究