Choudhuri D.; Tavares L.S.; L�pez J.A.�.2025-02-1720241http://dx.doi.org/10.1080/17476933.2024.2310217https://idr.iitbbs.ac.in/handle/2008/5496In this paper, the existence of at least one solution to the problem (Formula presented.) is established, where (Formula presented.) is the M-sub-Laplacian, (Formula presented.), (Formula presented.), (Formula presented.), ? is a bounded subset of the N-dimensional stratified Lie group (Formula presented.) with (Formula presented.) (N = 1, 2 has been avoided since they do not produce a purely stratified Lie group) and M is the homogeneous dimension of (Formula presented.). We will also show that in fact, the problem admits infinitely many solutions with some restrictions on the parameters involved. � 2024 Informa UK Limited, trading as Taylor & Francis Group.enCompactness; mountain pass geometry; stratified Lie group; Trudinger�Moser inequalityArticle