On radial solutions for a Fully Non Linear degenerate or singular PDE

Abstract

In this paper we consider equations $-|\nabla u{|}^{\alpha }F(D^{2}u)=|u{|}^{p-1}u$ in an annulus. $F$ is Fully Nonlinear Elliptic, $\alpha$ is some real $>-1$ and $p>1+\alpha$. 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.