4 citations · 17 across the 19 of their papers we have counts for
31 papers
On stable and finite Morse index solutions of the nonlocal Hénon-Gelfand-Liouville equation
Mostafa Fazly, Yeyao Hu, Wen Yang
We consider the nonlocal Hénon-Gelfand-Liouville problem for every , and . We prove a monotonici…
Partial regularity and Liouville theorems for stable solutions of anisotropic elliptic equations
Mostafa Fazly, Yuan Li
We study the quasilinear elliptic equation \begin{equation*} -Qu=e^u \ \ \text{in} \ \ Ω\subset \mathbb{R}^{N} \end{equation*} where the operator , known as Finsler-Laplacian (o…
On stable and finite Morse index solutions of the fractional Toda system
Mostafa Fazly, Wen Yang
We develop a monotonicity formula for solutions of the fractional Toda system when …
Classification of finite Morse index solutions of higher-order Gelfand-Liouville equation
Mostafa Fazly, Juncheng Wei, Wen Yang
We classify finite Morse index solutions of the following Gelfand-Liouville equation \begin{equation*} (-Δ)^{s} u= e^u \ \ \text{in} \ \ \mathbb{R}^n, \end{equation*} for a…
Analysis of propagation for impulsive reaction-diffusion models
Mostafa Fazly, Mark A. Lewis, Hao Wang
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 …
De Giorgi type results for equations with nonlocal lower-order terms
Mostafa Fazly
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, $$ Δu+ q\cdot \nabla u+f(u)=0 \ \ \t…
Regularity of extremal solutions of nonlocal elliptic systems
Mostafa Fazly
We examine regularity of the extremal solution of nonlinear nonlocal eigenvalue problem \begin{eqnarray} \left\{ \begin{array}{lcl} \hfill \mathcal L u &=& λF(u,v) \qquad \text{in}…
Symmetry properties for solutions of nonlocal equations involving nonlinear operators
Mostafa Fazly, Yannick Sire
We pursue the study of one-dimensional symmetry of solutions to nonlinear equations involving nonlocal operators. We consider a vast class of nonlinear operators and in a particula…
On nonlocal systems with jump processes of finite range and with decays
Mostafa Fazly, Changfeng Gui
We study the following system of equations when , and $H=(H_i)_{i=1}…
Stable solutions of symmetric systems involving hypoelliptic operators
Mostafa Fazly
Please see the article for the abstract.
Regularity of the extremal solutions associated to elliptic systems
A. Aghajani, C. Cowan
We examine the elliptic system given by \begin{eqnarray*} \qquad \left\{ \begin{array}{lcl} -Δu =λf(v) \quad \mbox{ in } Ω -Δv =γf(u) \quad \mbox{ in } Ω, u=v =0, \quad \mbox{ on }…
On impulsive reaction-diffusion models in higher dimensions
Mostafa Fazly, Mark Lewis, Hao Wang
Assume that denotes the density of the population at a point at the beginning of the reproductive season in the th year. We study the following impulsive reaction-d…
Monotonicity formulas for coupled elliptic gradient systems with applications
Mostafa Fazly, Henrik Shahgholian
Consider the following coupled elliptic system of equations \begin{equation*} \label{} (-Δ)^s u_i = (u^2_1+\cdots+u^2_m)^{\frac{p-1}{2}} u_i \quad \text{in} \ \ \mathbb{R}^n , \end…
One-dimensional symmetry for integral systems in two dimensions
Mostafa Fazly
The purpose of this brief paper is to prove De Giorgi type results for stable solutions of the following nonlocal system of integral equations in two dimensions $$ L(u_i) = H_i(u)…
Entire solutions of quasilinear symmetric systems
Mostafa Fazly
We study the following quasilinear elliptic system for all \begin{equation*} \label{} -div(Φ'(|\nabla u_i|^2) \nabla u_i) = H_i(u) \quad \text{in} \ \ \mathbb{R}^n \…
Stable solutions of symmetric systems on Riemannian manifolds
Mostafa Fazly
We examine stable solutions of the following symmetric system on a complete, connected, smooth Riemannian manifold without boundary, \begin{equation*} -Δ_g u_i = H_i(u…
Solutions of multi-component fractional symmetric systems
Mostafa Fazly
We study the following elliptic system concerning the fractional Laplacian operator when , $u_i…
Rigidity results for stable solutions of symmetric systems
Mostafa Fazly
We study stable solutions of the following nonlinear system where , and is a…
On stable solutions of the fractional Henon-Lane-Emden equation
Mostafa Fazly, Juncheng Wei
We derive monotonicity formulae for solutions of the fractional Hénon-Lane-Emden equation \begin{equation*} (-Δ)^{s} u=|x|^a |u|^{p-1} u \ \ \ \text{in } \ \ \mathbb{R}^n, \end{equ…
On finite Morse index solutions of higher order fractional Lane-Emden equations
Mostafa Fazly, Juncheng Wei
We classify finite Morse index solutions of the fractional Lane-Emden equation for . For the local case, and this cl…
Symmetry results for fractional elliptic systems and related problems
Mostafa Fazly, Yannick Sire
We study elliptic gradient systems with fractional laplacian operators on the whole space where…
Higher-dimensional solutions for a nonuniformly elliptic equation
Mostafa Fazly
We prove -dimensional symmetry results, that we call -Liouville theorems, for stable and monotone solutions of the following nonuniformly elliptic equation \begin{eqnarray*}\…
A pointwise inequality for the fourth order Lane-Emden equation
Mostafa Fazly, Juncheng Wei, Xingwang Xu
We prove that the following pointwise inequality holds \begin{equation*} -Δu \ge \sqrt\frac{2}{(p+1)-c_n} |x|^{\frac{a}{2}} u^{\frac{p+1}{2}} + \frac{2}{n-4} \frac{|\nabla u|^2}{u}…
Liouville theorems for the polyharmonic Henon-Lane-Emden system
Mostafa Fazly
We study Liouville theorems for the following polyharmonic Hénon-Lane-Emden system \begin{eqnarray*} \left\{\begin{array}{lcl} (-Δ)^m u&=& |x|^{a}v^p \ \ \text{in}\ \ \mathbb{R}^n,…