On subelliptic equations on stratified Lie groups driven by singular nonlinearity and weak $L^1$ data

TL;DR

This paper investigates elliptic equations on stratified Lie groups with singular nonlinearities and weak $L^1$ data, establishing the existence of solutions and infinitely many solutions under certain conditions.

Contribution

It extends the theory of subelliptic equations on stratified Lie groups by proving existence and multiplicity results with weak $L^1$ data and singular nonlinearities.

Findings

Existence of solutions for sub- and superlinear cases.

Infinitely many solutions for specific parameter ranges.

Application of the Symmetric Mountain Pass Theorem.

Abstract

The article is about an elliptic problem defined on a {\it stratified Lie group}. Both sub- and superlinear cases are considered whose solutions are guaranteed to exist in light of the interplay between the nonlinearities and the weak $L^1$ datum. The existence of infinitely many solutions is proved for suitable values of $\lambda,p,q$ by using the Symmetric Mountain Pass Theorem.