A direct method of moving planes for the fractional p-Laplacian system with negative powers
Indian Journal of Pure and Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Minghui Qie, Zhongxue Lü, Xin Zhang
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A direct method of moving planes for the fractional Laplacian
Advances in Mathematics, 2017 In this paper, we develop a direct method of moving planes for the fractional Laplacian. Instead of conventional extension method introduced by Caffarelli and Silvestre, we work directly on the non-local operator. Using the integral defining the fractional Laplacian, by an elementary approach, we first obtain the key ingredients needed in the method of
Chen, Wenxiong, Li, Congming, Li, Yan
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A direct method of moving planes for fully nonlinear nonlocal operators and applications
Discrete and Continuous Dynamical Systems - S, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Yuxia, Peng, Shaolong
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Direct method of moving planes for logarithmic Laplacian system in bounded domains
Discrete and Continuous Dynamical Systems, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baiyu Liu
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A direct method of moving planes for a fully nonlinear nonlocal system
Communications on Pure and Applied Analysis, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Pengyan, Niu, Pengcheng
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A direct method of moving planes for fractional Laplacian equations in the unit ball
Communications on Pure and Applied Analysis, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Moving planes and sliding methods for fractional elliptic and parabolic equations
Advanced Nonlinear StudiesIn this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions.
Chen Wenxiong, Hu Yeyao, Ma Lingwei
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A direct method of moving planes for logarithmic Schrödinger operator
Zeitschrift für Analysis und ihre Anwendungen, 2023 In this paper, we study the radial symmetry and monotonicity of nonnegative solutions to nonlinear equations involving the logarithmic Schrödinger operator (\mathcal{I}-\Delta)^{\log} corresponding to the logarithmic symbol
Rong Zhang +2 more
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Radially Symmetric Solution for Fractional Laplacian Systems with Different Negative Powers
Fractal and Fractional, 2022 By developing the direct method of moving planes, we study the radial symmetry of nonnegative solutions for a fractional Laplacian system with different negative powers: (−Δ)α2u(x)+u−γ(x)+v−q(x)=0,x∈RN, (−Δ)β2v(x)+v−σ(x)+u−p(x)=0,x∈RN, u(x)≳|x|a,v(x)≳|x ...
Haiyong Xu +3 more
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Liouville Type Theorems Involving the Fractional Laplacian on the Upper Half Euclidean Space
Fractal and Fractional, 2022 In this paper, we mainly establish Liouville-type theorems for the elliptic semi-linear equations involving the fractional Laplacian on the upper half of Euclidean space.
Tao Zhang
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