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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。
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.
期刊介绍：
The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications.
To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.
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