3 papers
math.AP2024
Asymptotically homogeneous solutions of the supercritical Lane-Emden system
Louis Dupaigne, Hatem Hajlaoui, Marius Ghergu
We consider the Lane-Emden system-u = |v| p-1 v,-v = |u| q-1 u in R d. When p q 1, it is known that there exists a positive radial stable solution (u, v) C…
math.AP2022
Liouville type theorems for solutions of the weighted fractional Lane-Emden system
Hatem Hajlaoui
In this paper, we prove Liouville type theorems for stable solutions to the weighted fractional Lane-Emden system \begin{align*} (-Δ)^s u = h(x)v^p,\quad (-Δ)^s v= h(x)u^q, \quad u…
math.AP2016
On the regularity and partial regularity of extremal solutions of a Lane-Emden system
Hatem Hajlaoui
In this paper, we consider the system on a smooth bounded domain in with the Dirichlet boundary condition on $\partial…