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arXiv · 2408.03788

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

Deepak Kumar Mahanta·Tuhina Mukherjee·Patrick Winkert
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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 $\mathbb{R}^N$. 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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Deepak Kumar Mahanta, Tuhina Mukherjee, Patrick Winkert. 2025-10-22. On singularly perturbed $(p, N )$-Laplace Schrödinger equation with logarithmic nonlinearity. https://doi.org/10.1515/ans-2023-0200

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