Sign-changing solutions of boundary value problems for semilinear Δ_γ​-Laplace equations

In this article, we study the multiplicity of weak solutions to the boundary value problem

{-G_α​u = g(x, y, u) + f(x, y, u) in Ω, u = 0 on ∂Ω,​

whereΩ is a bounded domain with smooth boundary in \ (N ≥ 2), α ∈ , g(x, y, ξ), f(x, y, ξ) are Carathéodory functions and G_α​ is the Grushin operator. We use the lower bounds of eigenvalues and an abstract theory on sign-changing solutions.