Least energy sign-changing solution for degenerate Kirchhoff double phase problems

In this paper we study the following nonlocal Dirichlet equation of double phase type−ψ∫Ω(|∇u|pp+μ(x)|∇u|qq)dxG(u)=f(x,u)in Ω,u=0on ∂Ω, where G is the double phase operator given byG(u)=div(|∇u|p−2∇u+μ(x)|∇u|q−2∇u)u∈W01,H(Ω), Ω⊆RN, N≥2, is a bounded domain with Lipschitz boundary ∂Ω, 10 and ϑ≥1, and f:Ω×R→R is a Carathéodory function that grows superlinearly and subcritically. We prove the existence of two constant sign solutions (one is positive, the other one negative) and of a sign-changing solution which turns out to be a least energy sign-changing solution of the problem above. Our proofs are based on variational tools in combination with the quantitative deformation lemma and the Poincaré-Miranda existence theorem.