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Existence of nontrivial solutions for fractional Choquard equations with critical or supercritical growth
Applicable Analysis ( IF 1.1 ) Pub Date : 2020-05-12 , DOI: 10.1080/00036811.2020.1761015
Quanqing Li 1 , Jian Zhang 2 , Wenbo Wang 3 , Kaimin Teng 4
Affiliation  

ABSTRACT

In this paper, we study the following fractional Choquard equation with critical or supercritical growth (Δ)su+V(x)u=[|x|μF(u)]f(u)+λ[|x|μ|u|p]p|u|p2u,xRN, where 0<s<1, (Δ)s denotes the fractional Laplacian of order s, N>2s, 0<μ<2s and p2μ,s:=(2Nμ)/(N2s). Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ>0 by the variational method.



中文翻译:

具有临界或超临界增长的分数 Choquard 方程的非平凡解的存在性

摘要

在本文中,我们研究了以下具有临界或超临界增长的分数 Choquard 方程(-Δ)s+(X)=[|X|-μ*F()]F()+λ[|X|-μ*||p]p||p-2,XRñ,其中 0< s <1,(-Δ)s表示s阶的分数拉普拉斯算子,N >2 s0<μ<2sp2μ,s*:=(2ñ-μ)/(ñ-2s). 在一些合适的条件下,我们证明了该方程对于小λ>0通过变分法。

更新日期:2020-05-12
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