Work

On the logarithmic p -Laplacian Schrödinger equation with multi-well potential: Multi-peak positive solutions

Year: 2025

Type: article

Abstract: This paper investigates the existence and multiplicity of multi-peak positive solutions for a class of p-Laplacian Schrödinger equations with logarithmic non-linearity in [Formula: see text]: [Formula: see text] Here, [Formula: see text] is a small parameter and the potential [Formula: see text] has multiple wells. The problem is characterized by the combined difficulties of the non-homogeneous p-Laplacian and a logarithmic term which prevents standard variational approaches. By combining a penalization method with variational techniques, we prove that for any non-empty set of potential wells, there exists a family of positive solutions. These solutions exhibit multiple peaks which concentrate at the minima of the potential as [Formula: see text]. This establishes the existence of at least [Formula: see text] distinct multi-peak solutions, where k is the number of wells, providing the first systematic result on the construction of such solutions for this class of quasilinear logarithmic problems.

Source: Bulletin of Mathematical Sciences

DOI: 10.1142/s1664360725500195

Authors: Lin Li, Huo Tao

Institution: Chongqing Technology and Business University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Natural Science Foundation Project of Chongqing, Chongqing Science and Technology Commission

Awards: G3596040873, G7504141522