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Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity
Mathematische Nachrichten ( IF 0.8 ) Pub Date : 2021-02-14 , DOI: 10.1002/mana.201900273
Guangze Gu 1, 2, 3 , Xianhua Tang 2 , Xianyong Yang 2
Affiliation  

In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity
a + b R 3 ( Δ ) s 2 u 2 d x ( Δ ) s u + V ( x ) u = Q ( x ) f ( u ) + | u | 2 s 2 u , x R 3 ,
where a , b > 0 , ( Δ ) s is the fractional Laplace operator with s ( 3 4 , 1 ) , V vanishes at infinity and 2 s = 6 3 2 s . Under appropriate assumptions on f, we prove the existence of positive solution by using the variational method.


中文翻译:

临界分数阶Kirchhoff方程正解的存在性,并且在无限大处可能消失

在本文中,我们考虑以下具有临界非线性的分数基尔霍夫方程
一种 + b [R 3 - Δ s 2个 ü 2个 d X - Δ s ü + 伏特 X ü = X F ü + | ü | 2个 s - 2个 ü X [R 3
在哪里 一种 b > 0 - Δ s 是带有分数的Laplace运算符 s 3 4 1个 V在无穷大处消失, 2个 s = 6 3 - 2个 s 。在关于f的适当假设下,我们使用变分方法证明了正解的存在。
更新日期:2021-04-11
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