9 papers
On the Classification of Stable Solutions of some elliptic equations in half-space
Foued Mtiri, Abdelbaki Selmi, Cherif Zaidi
In this paper, we are concerned with stable solutions , possibly unbounded and sign-changing, of some semi-linear elliptic problem with mixed nonlinear boundary conditions. We esta…
Liouville theorem on a half-space for biharmonic problem with Dirichlet boundary condition
Foued Mtiri, Abdelbaki Selmi, Cherif Zaid
We investigate here the nonlinear elliptic Hénon type equation: $$\D^{2} u= |x|^a|u|^{p-1}u \; \,\,\mbox{in}\,\,\,\, \R^{n}_{+}, \quad \quad u =\frac{\partial u}{\partial x_n} = 0…
Existence and nonexistence results of polyharmonic boundary value problems with supercritical growth
Abdellaziz Harrabi, Foued Mtiri, Wafa Mtaouaa
We establish some existence results of polyharmonic boundary value problems with supercritical growth. Our approach is based on truncation argument as well as -bounds.…
Liouville type theorems for stable solutions of elliptic system involving the Grushin operator
Foued Mtiri
We examine the degenerate elliptic system $$-Δ_{s} u = v^p, \quad -Δ_{s} v= u^θ, \quad u,v>0 \quad\mbox{in }\; \mathbb{R}^N=\mathbb{R}^{N_1}\times \mathbb{R}^{N_2}, \quad\mbox{wher…
Solutions of super-linear elliptic equations and their Morse indices
Foued Mtiri
We investigate here the degenerate bi-harmonic equation: $$Δ_{m}^2 u=f(x,u)\; \;\;\mbox{in} Ø,\quad u = Δu = 0\quad \mbox{on }\; \pΩ,$$ with and also the degenerate tri-h…
On the classification of solutions to a weighted elliptic system involving the Grushin operator
Foued Mtiri
We investigate here the following weighted degenerate elliptic system \begin{align*} -Δ_{s} u = \Big(1+\|\mathbf{x}\|^{2(s+1)}\Big)^{\fracα{2(s+1)}} v^p, \quad -Δ_{s} v = \Big(1+\|…