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|puin Ω,u=0on ∂Ω, where Ω⊂RN is a bounded Lipschitz domain, 10, respectively. Based on variational and topological tools such as truncation arguments and genus theory, we show the existence of λ⁎>0 such that the problem above has infinitely many weak solutions with negative energy values for any λ∈(0,λ⁎).
Farkas, C., Fiscella, A., Winkert, P. (2022). On a class of critical double phase problems. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 515(2 (15 November 2022)) [10.1016/j.jmaa.2022.126420].
On a class of critical double phase problems
Fiscella, Alessio
;
2022
Abstract
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|puin Ω,u=0on ∂Ω, where Ω⊂RN is a bounded Lipschitz domain, 10, respectively. Based on variational and topological tools such as truncation arguments and genus theory, we show the existence of λ⁎>0 such that the problem above has infinitely many weak solutions with negative energy values for any λ∈(0,λ⁎).
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