Two nontrivial solutions of boundary-value problems for semilinear Δ_γ-differential equations

摘要

In this paper, we study the existence of multiple solutions for the boundary-value problem Δ_γu+f(x,u)=0 inΩ, u=0 on ∂Ω, where Ω is a bounded domain with smooth boundary in R~N (N ≥ 2) and Δ_γ is the subelliptic operator of the type (Formula presented.). We use the three critical point theorem.