arXiv subjects

Mokhless Hammami

Publications and source records attributed to Mokhless Hammami.

4 recordsLinked to original sources

arXiv2004

Blowing up Solutions for a Biharmonic Equation with Critical Nonlinearity

In this paper we consider the following biharmonic equation with critical exponent $P_ε$ : $Δ^2 u= Ku^{(n+4)/(n-4)-ε}, u>0$ in $Ω$ and $u=Δu=0$ on $\partialΩ$, where $Ω$ is a domain in $R^n$, $n\geq 5$, $ε$ is a small positive parameter and $K$ is smooth positive function. We construct solutions of $P_ε$ which blow up and concentrate at strict local maximum of $K$ either at the boundary or in the interior of $Ω$. We also construct solutions of $P_ε$ concentrating at an interior strict local minimum of $K$. Finally, we prove a nonexistense result for the corresponding supercritical problem which is in sharp contrast with what happened for $P_ε$.

math.AP↗

arXiv2004

Some Existence Results for a Paneitz Type Problem Via the Theory of Critical Points at Infinity

In this paper a fourth order equation involving critical growth is considered under Navier boundary condition. We give some topological conditions on a given function to ensure the existence of solutions. Our methods involve the study of the critical points at infinity and their contribution to the topology of the level sets of the associated Euler Lagrange functional

math.AP↗

arXiv2004

On a Yamabe Type Problem on Three Dimensional Thin Annulus

We consider a Yamabe type problem on a family $A_ε$ of annulus shaped domains of $\R^3$ which becomes "thin" as $ε$ goes to zero. We show that, for any given positive constant $C$, there exists $ε_0$ such that for any $ε< ε_0$, the problem has no solution $u_ε$ whose energy is less than $C$. Such a result extends to dimension three a result previously known in higher dimensions. Although the strategy to prove this result is the same as in higher dimensions, we need a more careful and delicate blow up analysis of asymptotic profiles of solutions $u_ε$ when $ε$ goes to zero.

math.AP↗

arXiv2003

Nonexistence of Bounded Energy Solutions for a Fourth Order Equation on Thin Annuli

In this paper, we studu a biharmonic equation under the Navier boundary condition on thin annuli. We show that when the annulus becomes thin, the equation has no solution whose energy is bounded.

math.AP↗