Existence and multiplicity of solutions to Dirichlet problem for semilinear subelliptic equation with a free perturbation

TL;DR

This paper establishes the existence and multiple solutions for a semilinear subelliptic Dirichlet problem with free perturbation, using advanced embedding theorems, eigenvalue estimates, and minimax methods.

Contribution

It introduces new existence and multiplicity results for subelliptic equations with free perturbations, employing novel analytical techniques.

Findings

Proved existence of weak solutions under certain conditions.

Established multiple solutions using minimax methods.

Derived lower bounds for Dirichlet eigenvalues.

Abstract

This paper is concerned with existence and multiplicity results for the semilinear subelliptic equation with free perturbation term. By using the degenerate Rellich-Kondrachov compact embedding theorem, precise lower bound estimates of Dirichlet eigenvalues for the finitely degenerate elliptic operator and minimax method, we obtain the existence and multiplicity of weak solutions for the problem.