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On singularly perturbed $(p, n )$-Laplace Schr\"{o}dinger equation with logarithmic nonlinearity by Mahanta, Deepak Kumar; Mukherjee, Tuhina; Winkert, Patrick is a scholarly article available to read on EtoBox.

What is On singularly perturbed $(p, n )$-Laplace Schr\"{o}dinger equation with logarithmic nonlinearity about?

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 Schr\"{o}dinger 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.

Author

Mahanta, Deepak Kumar; Mukherjee, Tuhina; Winkert, Patrick

Published

2024

Language

EN