Results 111 to 120 of about 5,262 (196)

ON FRACTIONAL DUNKL-TYPE LAPLACIAN [PDF]

This thesis provides a comprehensive study of the fractional Dunkl-type Laplacian operator (—llxllΔk) σ for 0 \u3c σ \u3c 1, focusing on four key equivalent characterizations: the heat semigroup approach, the pointwise formulation, the spherical mean ...
Aldan, Saba Ibrahim
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Numerical investigation on nonlocal problems with the fractional Laplacian [PDF]

, 2017
Nonlocal models have recently become a powerful tool for studying complex systems with long-range interactions or memory effects, which cannot be described properly by the traditional differential equations.
Duo, Siwei
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Bifurcation and multiplicity of solutions for the fractional Laplacian with critical exponential nonlinearity

Electronic Journal of Differential Equations, 2016
We study the fractional elliptic equation $$\displaylines{ (-\Delta)^{1/2} u = \lambda u+|u|^{p-2}ue^{u^2} ,\quad\text{in } (-1,1),\cr u=0\quad\text{in } \mathbb{R}\setminus(-1,1), }$$ where $\lambda$ is a positive real parameter, p>2 and $(-\Delta)^
Pawan Kumar Mishra, Konijeti Sreenadh
doaj  

Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian. [PDF]

J Inequal Appl, 2018
Qu M, Yang L.
europepmc   +1 more source

A Space–Time Spectral Method for Nonlinear Fractional Convection–Diffusion Equations with Viscosity Terms

Fractal and Fractional
We develop a high-order space-time spectral method for nonlinear convection–diffusion equations with a Riemann–Liouville time-fractional derivative and a spectrally defined space-fractional Laplacian.
Zhe Yu, Shanshan Guo, Xinming Zhang, Baohe Zhang   +3 more
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Existence of solutions for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities

Electronic Journal of Differential Equations, 2019
In this work, we establish the existence of solutions for the nonlinear nonlocal system of equations involving the fractional Laplacian, \begin{gather*} \begin{aligned} (-\Delta)^s u & = au+bv+\frac{2p}{p+q}\int_{\Omega}\frac{|v(y)|^q}{|x-y|^\mu}dy|
Yang Yang, Qian Yu Hong, Xudong Shang
doaj  

The properties of a new fractional g-Laplacian Monge-Ampère operator and its applications

Advances in Nonlinear Analysis
In this article, we first introduce a new fractional gg-Laplacian Monge-Ampère operator: Fgsv(x)≔infP.V.∫Rngv(z)−v(x)∣C−1(z−x)∣sdz∣C−1(z−x)∣n+s∣C∈C,{F}_{g}^{s}v\left(x):= \inf \left\{\hspace{0.1em}\text{P.V.}\hspace{0.1em}\mathop{\int }\limits_{{{\mathbb{
Wang Guotao, Yang Rui, Zhang Lihong
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Fractional revival of threshold graphs under Laplacian dynamics [PDF]

, 2019
Let $X$ be a graph, and denote its Laplacian matrix by $L$. Let $U(t) = e^{itL}$. Then $U(t)$ is a complex symmetric unitary matrix. We say that $X$ admits Laplacian fractional revival between vertices $j$ and $k$ at time $t = t_0$, if $U(t_0)e_j ...
Zhang, Xiaohong
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Epiperimetric inequalities in the obstacle problem for the fractional Laplacian. [PDF]

Calc Var Partial Differ Equ
Carducci M.
europepmc   +1 more source

Fractional Laplacian in conformal geometry [PDF]

In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli and Silvestre and a class of conformally covariant operators in conformal geometry.Peer ...
González Nogueras, María del Mar, Chang, Sun-Yung Alice   +1 more
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