Non-existence of positive solutions for a higher order fractional equation
Non-existence of positive solutions for a higher order fractional equation
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DOI：
10.3934/dcds.2019059
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Xuewei Cui;Mei Yu
中科院分区：
文献类型：
--
作者：
Xuewei Cui;Mei Yu
本文考虑全空间上一类含有高阶分数次拉普拉斯的非线性方程。利用极大值原理和刘维尔定理建立了伪微分方程与积分方程解的等价性。对于方程的正解，我们应用移动平面法得到了正解的不存在性。
In this paper, we consider a nonlinear equation involving fractional Laplacian of higher order on the whole space. We establish the equivalence between the pseudo-differential equation and an integral equation by applying the maximum principle and the Liouville theorem. For positive solutions to the equation, we obtained non-existence by applying the method of moving planes.