4 citations · 17 across the 19 of their papers we have counts for
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Uniqueness of solutions for a nonlocal elliptic eigenvalue problem
Craig Cowan, Mostafa Fazly
We examine equations of the form {eqnarray*} \{{array}{lcl} \hfill \HA u &=& λg(x) f(u) \qquad \text{in}\ Ω\hfill u&=& 0 \qquad \qquad \qquad \text{on}\ \pOm, {array}. {eqnarray*}…
Effect of weights on stable solutions of a quasilinear elliptic equation
Mostafa Fazly
In this note, we study Liouville theorems for the stable and finite Morse index weak solutions of the quasilinear elliptic equation in where $p\…
Liouville type theorems for stable solutions of certain elliptic systems
Mostafa Fazly
We establish Liouville type theorems for elliptic systems with various classes of non-linearities on . We show among other things, that a system has no semi-stable so…
On stable entire solutions of semi-linear elliptic equations with weights
Craig Cowan, Mostafa Fazly
We are interested in the existence versus non-existence of non-trivial stable sub- and super-solutions of {equation} \label{pop} -div(ω_1 \nabla u) = ω_2 f(u) \qquad \text{in}\ \ \…
On the Hénon-Lane-Emden conjecture
Mostafa Fazly, Nassif Ghoussoub
We consider Liouville-type theorems for the following Hénon-Lane-Emden system \hfill -Δu&=& |x|^{a}v^p \text{in} \mathbb{R}^N, \hfill -Δv&=& |x|^{b}u^q \text{in} \mathbb{R}^N, when…