一类分数阶$p$-拉普拉斯问题非平凡解的多重性

Pub Date : 2015-07-08 DOI:10.4171/ZAA/1541

Ghanmi Abdeljabbar

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引用次数: 12

摘要

．本文讨论了分数阶p -拉普拉斯问题的非平凡解的存在性，该问题的类型为:Ω是rn中具有光滑边界∂Ω的有界域，a∈C (Ω)， p≥2，α∈(0,1)，使得pα < n, 1 < q < p < R < npn - αp, F∈c1 (Ω × R, R)。利用Nehari流形的分解，证明了非局部椭圆型问题至少有两个非平凡解。

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Multiplicity of Nontrivial Solutions of a Class of Fractional $p$-Laplacian Problem

. In this paper, we deal with existence of nontrivial solutions to the fractional p -Laplacian problem of the type where Ω is a bounded domain in R n with smooth boundary ∂ Ω, a ∈ C (Ω), p ≥ 2, α ∈ (0 , 1) such that pα < n , 1 < q < p < r < npn − αp , and F ∈ C 1 (Ω × R , R ). Using the decomposition of the Nehari manifold, we prove that the non-local elliptic problem has at least two nontrivial solutions.

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