arXiv subjects
Publications and source records attributed to Cheikhou Oumar Ndaw.
In this paper we consider equations $-| \nabla u |^αF ( D^2 u) = |u|^{p-1} u $ in an annulus. $F$ is Fully Nonlinear Elliptic, $α$ is some real $> -1$ and $p > 1+ α$. The solutions are intended in the sense of the definition given by Birindelli and Demengel \cite{BD1}. We prove the existence of non trivial positive/negative radial solutions.
In this article we prove existence, uniqueness and regularity for the singular equation \begin{eqnarray*} \begin{cases} |\nabla u|^α(F(D^{2}u)+h(x)\cdot\nabla u)+c(x)|u|^αu+p(x)u^{-γ}=0 \ \mbox{ in } \ Ω\\ u>0 \ \mbox{ in } \ Ω, \ u=0 \ \mbox{ on } \ \partialΩ\end{cases} \end{eqnarray*} when $p$ is some continuous and positive function, $c$ and $h$ are continuous, $α> -1$ and $F$ is Fully non linear elliptic. Some conditions on the first eigenvalue for the operator $|\nabla u|^α(F(D^{2}u)+h(x)\cdot\nabla u)+c(x)|u|^αu$ are required. The results generalizes the well known results of Lazer and Mac Kenna.