Multiple solutions for a fractional elliptic problem with critical growth

Autor: Dumitru Motreanu, F.R. Pereira, Olímpio H. Miyagaki
Přispěvatelé: Universidade Federal de Juiz de Fora (UFJF), Département de Mathématiques (IREM), Université Montpellier 2 - Sciences et Techniques (UM2)
Rok vydání: 2020
Předmět:
Zdroj: Journal of Differential Equations
Journal of Differential Equations, Elsevier, 2020, 269, pp.5542-5572. ⟨10.1016/j.jde.2020.04.010⟩
ISSN: 0022-0396
1090-2732
Popis: The paper focuses on a nonlocal Dirichlet problem with asymmetric nonlinearities. The equation is driven by the fractional Laplacian ( − Δ ) s for s ∈ ( 0 , 1 ) and exhibits a sublinear term containing a parameter λ, a linear term interfering with the spectrum of ( − Δ ) s and a superlinear term with fractional critical growth. The corresponding local problem governed by the standard Laplacian operator was investigated by F. O. de Paiva and A. E. Presoto. It can be recovered by letting s ↑ 1 . The statement given here in the nonlocal setting is also related to extensively studied topics for local elliptic operators as the Brezis-Nirenberg problem and asymmetric nonlinearities. We go beyond the case of the standard Laplacian taking advantage of recent contributions on nonlocal fractional equations. Our main result establishes the existence of at least three nontrivial solutions, with one nonnegative and one nonpositive, provided the parameter λ > 0 is sufficiently small. In order to overcome the difficulties in the nonlocal setting we develop new arguments that are substantially different from those used in previous works.
Databáze: OpenAIRE
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