Work

A critical elliptic equation with a logarithmic type perturbation

Year: 2025

Type: article

Abstract: In this note, we consider a critical elliptic equation perturbed by a logarithmic type subcritical term in R 4 , and investigate how the logarithmic term affects the existence of weak solutions to such a problem. Since the logarithmic term does not satisfy the standard monotonicity condition, essential difficulty arises when one looks for weak solutions to this problem in the variational framework. After some delicate estimates on the logarithmic term we can control the mountain pass level of the corresponding functional so that it satisfies the local compactness condition. Then a positive weak solution follows with the application of the Mountain Pass Lemma and Brézis–Lieb lemma. Our result implies that the logarithmic term plays a positive role for the problem to admit positive solutions.

Source: Electronic journal of qualitative theory of differential equations

DOI: 10.14232/ejqtde.2025.1.5

Authors: Haixia Li, Yuzhu Han

Institutions: Changchun Normal University, Jilin University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Changchun Normal University, National Key Research and Development Program of China

Awards: G3406403891, G5704951092, G5861325694, G606463691