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

In this paper we consider equations $-\mathrm{\mid }\mathrm{\nabla }u{\mathrm{\mid }}^{\alpha }F(D^{2}u)=\mathrm{\mid }u{\mathrm{\mid }}^{p-1}u$ 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.