A direct method of moving planes for the fractional Laplacian [PDF]
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
exaly +7 more sources
Direct method of moving planes for logarithmic Laplacian system in bounded domains
Discrete & Continuous Dynamical Systems - A, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Baiyu Liu
exaly +5 more sources
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
exaly +5 more sources
A direct method of moving planes for a fully nonlinear nonlocal system
Communications on Pure & Applied Analysis, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Pengyan, Niu, Pengcheng
exaly +6 more sources
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.
Meixia Dou
exaly +6 more sources
A direct method of moving planes for logarithmic Schrödinger operator [PDF]
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
+10 more sources
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
openaire +4 more sources
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
doaj +1 more source
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
doaj +1 more source
Symmetry of standing waves for two kinds of fractional Hardy-Schrödinger equations
Alexandria Engineering Journal, 2021 In this paper, we consider two kinds of nonlinear Schrödinger equations with the fractional Laplacian and Hardy potential (λ|x|s ...
Guotao Wang +3 more
doaj +1 more source