On a class of critical double phase problems

In this paper we study a class of double phase problems involving critical growth, namely−div(|∇u|p−2∇u+μ(x)|∇u|q−2∇u)=λ|u|ϑ−2u+|u|p⁎−2uin Ω,u=0on ∂Ω, where Ω⊂RN is bounded Lipschitz domain, 1<ϑ0, respectively. Based on variational topological tools such as truncation arguments genus theory, show existence λ⁎>0 that problem above has infinitely many weak solutions with negative energy values for any λ∈(0,λ⁎).