4 papers
Bubbles clustered inside for almost critical problems
Mohamed Ben Ayed, Khalil El Mehdi
We investigate the existence of blowing-up solutions of the following almost critical problem $$ -Δu +V(x)u =u^{p-\e},\quad u>0\quad\mbox{in}\quad Ø,\quad u=0\quad\mbox{on}\quad \p…
Multi-Bubble Blow-up Analysis for an Almost Critical Problem
Mohamed Ben Ayed, Khalil El Mehdi
Consider a smooth, bounded domain with and a smooth positive function . We analyze the asymptotic behavior of a sequence of positive solutions…
On the Nirenberg problem on spheres: Arbitrarily many solutions in a perturbative setting
Mohameden Ahmedou, Mohamed Ben Ayed, Khalil El Mehdi
Given a smooth positive function on the standard sphere , we use Morse theoretical methods and counting index formulae to prove that, under generic conditio…
Nirenberg problem on high dimensional spheres: Blow up with residual mass phenomenon
Mohameden Ahmedou, Mohamed Ben Ayed, Khalil El Mehdi
In this paper, we extend the analysis of the subcritical approximation of the Nirenberg problem on spheres recently conducted in \cite{MM19, MM}. Specifically, we delve into the sc…