Results 1 to 10 of about 15,610 (84)

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, Vishvesh Kumar, Michael Ruzhansky   +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, Bashir Ahmad, Guotao Wang, Lihong Zhang   +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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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, Xueyan Ren, Lihong Zhang, Bashir Ahmad   +3 more
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Radial symmetry for a generalized nonlinear fractional p-Laplacian problem

Nonlinear Analysis, 2021
This paper first introduces a generalized fractional p-Laplacian operator (–Δ)sF;p. By using the direct method of moving planes, with the help of two lemmas, namely decay at infinity and narrow region principle involving the generalized fractional p ...
Wenwen Hou, Lihong Zhang, Ravi P. Agarwal, Guotao Wang   +3 more
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Radial symmetry of a relativistic Schrödinger tempered fractional p-Laplacian model with logarithmic nonlinearity

Nonlinear Analysis, 2022
In this paper, by introducing a relativistic Schrödinger tempered fractional p-Laplacian operator (–Δ)p,λs,m, based on the relativistic Schrödinger operator (–Δ + m2)s and the tempered fractional Laplacian (Δ + λ)β/2, we consider a relativistic ...
Wenwen Hou, Lihong Zhang
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Monotonicity results for the fractional p-Laplacian in unbounded domains

Bulletin of Mathematical Sciences, 2021
In this paper, we develop a direct method of moving planes in unbounded domains for the fractional p-Laplacians, and illustrate how this new method to work for the fractional p-Laplacians.
Leyun Wu, Mei Yu, Binlin Zhang
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A direct method of moving planes for fully nonlinear nonlocal operators and applications

Discrete and Continuous Dynamical Systems - S, 2021
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Guo, Yuxia, Peng, Shaolong
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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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Properties of solutions to fractional p-subLaplace equations on the Heisenberg group

Boundary Value Problems, 2020
The aim of this paper is to study properties of solutions to the fractional p-subLaplace equations on the Heisenberg group. Based on the maximum principles and the generalization of the direct method of moving planes, we obtain the symmetry and ...
Xinjing Wang, Guangwei Du
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