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pro vyhledávání: '"Fazly, Mostafa"'
We consider the nonlocal H\'{e}non-Gelfand-Liouville problem $$ (-\Delta)^s u = |x|^a e^u\quad\mathrm{in}\quad \mathbb R^n, $$ for every $s\in(0,1)$, $a>0$ and $n>2s$. We prove a monotonicity formula for solutions of the above equation using rescalin
Externí odkaz:
http://arxiv.org/abs/2008.07374
Autor:
Fazly, Mostafa, Li, Yuan
We study the quasilinear elliptic equation \begin{equation*} -Qu=e^u \ \ \text{in} \ \ \Omega\subset \mathbb{R}^{N} \end{equation*} where the operator $Q$, known as Finsler-Laplacian (or anisotropic Laplacian), is defined by $$Qu:=\sum_{i=1}^{N}\frac
Externí odkaz:
http://arxiv.org/abs/2008.04455
Autor:
Fazly, Mostafa, Yang, Wen
We develop a monotonicity formula for solutions of the fractional Toda system $$ (-\Delta)^s f_\alpha = e^{-(f_{\alpha+1}-f_\alpha)} - e^{-(f_\alpha-f_{\alpha-1})} \quad \text{in} \ \ \mathbb R^n,$$ when $0
Externí odkaz:
http://arxiv.org/abs/2007.00069
We classify finite Morse index solutions of the following Gelfand-Liouville equation \begin{equation*} (-\Delta)^{s} u= e^u \ \ \text{in} \ \ \mathbb{R}^n, \end{equation*} for $1
Externí odkaz:
http://arxiv.org/abs/2006.06089
Akademický článek
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We study a hybrid impulsive reaction-advection-diffusion model given by a reaction-advection-diffusion equation composed with a discrete-time map in space dimension $n\in\mathbb N$. The reaction-advection-diffusion equation takes the form \begin{equa
Externí odkaz:
http://arxiv.org/abs/1912.08711
Autor:
Fazly, Mostafa
It is known that the De Giorgi's conjecture does not hold in two dimensions for semilinear elliptic equations with a nonzero drift, in general, $$ \Delta u+ q\cdot \nabla u+f(u)=0 \ \ \text{in } \ \ \mathbb R^2, $$ when $q=(0,-c)$ for $c\neq 0$. This
Externí odkaz:
http://arxiv.org/abs/1905.13193
Autor:
Fazly, Mostafa
We examine regularity of the extremal solution of nonlinear nonlocal eigenvalue problem \begin{eqnarray} \left\{ \begin{array}{lcl} \hfill \mathcal L u &=& \lambda F(u,v) \qquad \text{in} \ \ \Omega, \\ \hfill \mathcal L v &=& \gamma G(u,v) \qquad \t
Externí odkaz:
http://arxiv.org/abs/1902.04640
Autor:
Fazly, Mostafa, Sire, Yannick
We pursue the study of one-dimensional symmetry of solutions to nonlinear equations involving nonlocal operators. We consider a vast class of nonlinear operators and in a particular case it covers the fractional $p-$Laplacian operator. Just like the
Externí odkaz:
http://arxiv.org/abs/1807.06189
Autor:
Fazly, Mostafa, Gui, Changfeng
We study the following system of equations $$ L_i(u_i) = H_i(u_1,\cdots,u_m) \quad \text{in} \ \ \mathbb R^n , $$ when $m\ge 1$, $u_i: \mathbb R^n \to \mathbb R$ and $H=(H_i)_{i=1}^m$ is a sequence of general nonlinearities. The nonlocal operator $L_
Externí odkaz:
http://arxiv.org/abs/1807.06187