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.
2022

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11566/305961
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