On singularly perturbed (p, N )-Laplace Schrödinger equation with logarithmic nonlinearity

2024/08/07 by Deepak Kumar Mahanta, Mahanta, Deepak Kumar, Tuhina Mukherjee +3
Mathematics · #35A15 #35D30 #35J10 #35J60 #35J92 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2408.03788

openalex publication_date 2024/08/07 · openalex created_date 2024/11/01 · openalex updated_date 2026/07/28

Abstract

This article focuses on the study of the existence, multiplicity and concentration behavior of ground states as well as the qualitative aspects of positive solutions for a (p, N)-Laplace Schrödinger equation with logarithmic nonlinearity and critical exponential nonlinearity in the sense of Trudinger-Moser in the whole Euclidean space ℝ^N. Through the use of smooth variational methods, penalization techniques, and the application of the Lusternik-Schnirelmann category theory, we establish a connection between the number of positive solutions and the topological properties of the set in which the potential function achieves its minimum values.

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