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

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.