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 ℝ𝑁 . 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 a set in which the potential function achieves its minimum values.
Mahanta et al. (Tue,) studied this question.