In this paper we focus on the following nonlocal problem with critical growth: {(-Δ)su=λu+u+2s∗-1+f(x)inΩ,u=0inRN\Ω,where s∈ (0 , 1) , N> 2 s, Ω ⊂ RN is a smooth bounded domain, λ> 0 , (- Δ) s is the fractional Laplacian, f= te1+ h where t∈ R, e1 is the first eigenfunction of (- Δ) s with homogeneous Dirichlet boundary datum, and h∈ L∞(Ω) is such that ∫Ωhe1dx=0. According to the interaction of the nonlinear term with the spectrum of (- Δ) s, we establish some existence and multiplicity results for the above problem by means of variational methods.
The critical fractional Ambrosetti–Prodi problem / Ambrosio, V.; Isernia, T.. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - (2022). [10.1007/s12215-022-00757-4]
The critical fractional Ambrosetti–Prodi problem
Ambrosio V.;Isernia T.
2022-01-01
Abstract
In this paper we focus on the following nonlocal problem with critical growth: {(-Δ)su=λu+u+2s∗-1+f(x)inΩ,u=0inRN\Ω,where s∈ (0 , 1) , N> 2 s, Ω ⊂ RN is a smooth bounded domain, λ> 0 , (- Δ) s is the fractional Laplacian, f= te1+ h where t∈ R, e1 is the first eigenfunction of (- Δ) s with homogeneous Dirichlet boundary datum, and h∈ L∞(Ω) is such that ∫Ωhe1dx=0. According to the interaction of the nonlinear term with the spectrum of (- Δ) s, we establish some existence and multiplicity results for the above problem by means of variational methods.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
