arXiv subjects

Abdelbaki Selmi

Publications and source records attributed to Abdelbaki Selmi.

2 recordsLinked to original sources

arXiv2021

Liouville theorem on a half-space for biharmonic problem with Dirichlet boundary condition

We investigate here the nonlinear elliptic Hénon type equation: $$\D^{2} u= |x|^a|u|^{p-1}u \; \,\,\mbox{in}\,\,\,\, \R^{n}_{+}, \quad \quad u =\frac{\partial u}{\partial x_n} = 0 \quad \mbox{in}\,\,\,\, \partial \R^{n}_{+},$$ with $p>1$ and $n\geq 2$. In particular, we prove some Liouville type theorems for stable at infinity solutions. The main methods used are the integral estimates, the Pohozaev-type identity and the monotonicity formula.

math.AP↗

arXiv2021

On the Classification of Stable Solutions of some elliptic equations in half-space

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 establish the nonexistence of stable solutions, the main methods used are the Pohozaev identity, monotonicity formula of solutions together with a blowing down sequence.

math.AP↗