Nonlinear elliptic PDEs arise naturally in diverse areas such as engineering, geometry, materials science, physics, and topology. The present seminar addresses an elliptic problem defined by a stratified Lie group. Both sub and superlinear cases have been considered whose solutions have been guaranteed to exist in light of the interplay between the nonlinearities and the weak Lebsegue function. The existence of infinitely many solutions has been proved using the symmetric mountain pass theorem.

Keywords: Stratified Lie Group, Subelliptic operators, Marcinkiewicz space, Singular problem.