The paper deals with the following double phase problem -m[∫Ω(|∇u|pp+a(x)|∇u|qq)dx]div(|∇u|p-2∇u+a(x)|∇u|q-2∇u)=λu-γ+up∗-1inΩ,u>0inΩ,u=0on∂Ω,where Ω ⊂ RN is a bounded domain with Lipschitz boundary ∂Ω , N≥ 2 , m represents a Kirchhoff coefficient, 1 < p< q< p∗ with p∗= Np/ (N- p) being the critical Sobolev exponent to p, a bounded weight a(·) ≥ 0 , λ> 0 and γ∈ (0 , 1). By the Nehari manifold approach, we establish the existence of at least one weak solution.
Arora, R., Fiscella, A., Mukherjee, T., Winkert, P. (2022). On critical double phase Kirchhoff problems with singular nonlinearity. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 71(3), 1079-1106 [10.1007/s12215-022-00762-7].
On critical double phase Kirchhoff problems with singular nonlinearity
Fiscella, Alessio;
2022
Abstract
The paper deals with the following double phase problem -m[∫Ω(|∇u|pp+a(x)|∇u|qq)dx]div(|∇u|p-2∇u+a(x)|∇u|q-2∇u)=λu-γ+up∗-1inΩ,u>0inΩ,u=0on∂Ω,where Ω ⊂ RN is a bounded domain with Lipschitz boundary ∂Ω , N≥ 2 , m represents a Kirchhoff coefficient, 1 < p< q< p∗ with p∗= Np/ (N- p) being the critical Sobolev exponent to p, a bounded weight a(·) ≥ 0 , λ> 0 and γ∈ (0 , 1). By the Nehari manifold approach, we establish the existence of at least one weak solution.
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