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Monotonicity of positive solutions for fractional p-systems in unbounded Lipschitz domains
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-04-10 , DOI: 10.1016/j.na.2020.111892
Lingwei Ma , Zhenqiu Zhang

In this paper, without imposing any decay assumptions on the solutions at infinity, we first develop an unbounded narrow region principle for the fractional p-Laplacian systems, an essential ingredient to carry on the direct method of moving planes; then we combine this direct method with the sliding method to obtain the monotonicity of positive bounded solutions for cooperative systems involving the fractional p-Laplacian in unbounded Lipschitz domains. We believe that the new ideas introduced here will become useful tools in studying qualitative properties of solutions for other types of nonlinear nonlocal systems in various unbounded domains.



中文翻译:

分数阶正解的单调性 pLipschitz域中的无穷系统

在本文中,在不对无穷大解施加任何衰减假设的情况下,我们首先针对分数阶建立了无界窄域原理 p拉普拉斯系统,是进行飞机直接运动的基本要素;然后将这种直接方法与滑动方法结合起来,以获得涉及分数阶的合作系统的正有界解的单调性p-无界Lipschitz域中的Laplacian。我们相信,这里介绍的新思想将成为研究各种无界域中其他类型的非线性非局部系统解的定性性质的有用工具。

更新日期:2020-04-10
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