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&gt;0inΩ,u=0on∂Ω,where Ω ⊂ RN is a bounded domain with Lipschitz boundary ∂Ω , N≥ 2 , m represents a Kirchhoff coefficient, 1 &lt; p&lt; q&lt; p∗ with p∗= Np/ (N- p) being the critical Sobolev exponent to p, a bounded weight a(·) ≥ 0 , λ&gt; 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

#### 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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Articolo in rivista - Articolo scientifico
Critical growth; Double phase operator; Fibering method; Nehari manifold; Nonlocal Kirchhoff term; Singular problem;
English
1-giu-2022
2022
71
3
1079
1106
open
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/380520`