Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball

Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball

In this paper, we study a nonlinear system involving the fractional p-Laplacian in a unit ball and establish the radial symmetry and monotonicity of its positive solutions. By using the direct method of moving planes, we prove the following result. For 0<s,t<1,p>0, if u and v satisfy the fo...

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Main Authors: Linfen Cao, Xiaoshan Wang, Zhaohui Dai
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2018/1565731
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spelling doaj-8fcbe7eb57b5437ea6c8f7660dd1b4d92021-07-02T17:12:12ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/15657311565731Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a BallLinfen Cao0Xiaoshan Wang1Zhaohui Dai2Henan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaHenan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaHenan Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaIn this paper, we study a nonlinear system involving the fractional p-Laplacian in a unit ball and establish the radial symmetry and monotonicity of its positive solutions. By using the direct method of moving planes, we prove the following result. For 0<s,t<1,p>0, if u and v satisfy the following nonlinear system -Δpsux=fvx;  -Δptvx=gux,  x∈B10;  ux,vx=0,  x∉B10. and f,g are nonnegative continuous functions satisfying the following: (i) f(r) and g(r) are increasing for r>0; (ii) f′(r)/rp-2, g′(r)/rp-2 are bounded near r=0. Then the positive solutions (u,v) must be radially symmetric and monotone decreasing about the origin.http://dx.doi.org/10.1155/2018/1565731
collection DOAJ
language English
format Article
sources DOAJ
author Linfen Cao
Xiaoshan Wang
Zhaohui Dai
spellingShingle Linfen Cao
Xiaoshan Wang
Zhaohui Dai
Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball
Advances in Mathematical Physics
author_facet Linfen Cao
Xiaoshan Wang
Zhaohui Dai
author_sort Linfen Cao
title Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball
title_short Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball
title_full Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball
title_fullStr Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball
title_full_unstemmed Radial Symmetry and Monotonicity of Solutions to a System Involving Fractional p-Laplacian in a Ball
title_sort radial symmetry and monotonicity of solutions to a system involving fractional p-laplacian in a ball
publisher Hindawi Limited
series Advances in Mathematical Physics
issn 1687-9120
1687-9139
publishDate 2018-01-01
description In this paper, we study a nonlinear system involving the fractional p-Laplacian in a unit ball and establish the radial symmetry and monotonicity of its positive solutions. By using the direct method of moving planes, we prove the following result. For 0<s,t<1,p>0, if u and v satisfy the following nonlinear system -Δpsux=fvx;  -Δptvx=gux,  x∈B10;  ux,vx=0,  x∉B10. and f,g are nonnegative continuous functions satisfying the following: (i) f(r) and g(r) are increasing for r>0; (ii) f′(r)/rp-2, g′(r)/rp-2 are bounded near r=0. Then the positive solutions (u,v) must be radially symmetric and monotone decreasing about the origin.
url http://dx.doi.org/10.1155/2018/1565731
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AT xiaoshanwang radialsymmetryandmonotonicityofsolutionstoasysteminvolvingfractionalplaplacianinaball
AT zhaohuidai radialsymmetryandmonotonicityofsolutionstoasysteminvolvingfractionalplaplacianinaball
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