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A critical fractional equation with concave–convex power nonlinearities

2014; Elsevier BV; Volume: 32; Issue: 4 Linguagem: Inglês

10.1016/j.anihpc.2014.04.003

ISSN

1873-1430

Autores

Begoña Barrios, Eduardo Colorado, Raffaella Servadei, Fernando Soria,

Tópico(s)

Fractional Differential Equations Solutions

Resumo

In this work we study the following fractional critical problemwhere Ω ⊂ R n is a regular bounded domain, λ > 0, 0 < s < 1 and n > 2s.Here (-) s denotes the fractional Laplace operator defined, up to a normalization factor, byOur main results show the existence and multiplicity of solutions to problem (P λ ) for different values of λ.The dependency on this parameter changes according to whether we consider the concave power case (0 < q < 1) or the convex power case (1 < q < 2 * s -1).These two cases will be treated separately.

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