On a weighted N-Laplacian problem with double exponential nonlinearities
Year: 2025
Type: article
Abstract: In this paper, we study the nonlinear elliptic problem -\operatorname{div}\bigl(w(x)|\nabla u|^{N-2}\nabla u\bigr)=f(x,u),\quad u\in W_0^{1,N}(B,w)\quad(P) where B is the unit ball of \mathbb{R}^N , N\ge 2 and w(x)=\bigl(\log\frac{e}{|x|}\bigr)^{N-1} is the singular logarithm weight with the limiting exponent N-1 in the Trudinger-Moser embedding. We consider the problem (P) when the nonlinearity is sub-critical and critical with respect to a maximal growth of double exponent type and we prove the existence of positive solution by using Mountain Pass theorem without the Ambrosetti-Rabinowitz condition. When the nonlinearity is critical, we prove that the associated energy satisfies the Palais-Smale condition only to a given limit level and we prove that the min-max level is less than this limit.
Source: Filomat
DOI: 10.2298/fil2525651d
Authors: Brahim Dridi, Rached Jaidane
Institutions: Tunis University, Tunis El Manar University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7149607366