On the Existence of Radial Solutions of a Nonlinear Elliptic BVP in an Annulus

In this paper we study the radial solutions of quasilinear elliptic BVP:\documentclass{article}\pagestyle{empty}\begin{document}$ div (a(|x|,\,u,|\nabla u|)\nabla u) + f(|x|,\,u,\,|\nabla u|) = 0 $\end{document} on A , u satisfies the Robin boundary conditions (2) below, where A = { x ∈ R n ; a 1 < | x | < a 2 }, a 2 > a 1 > 0, constants. Under the very general conditions, we prove that if f is superlinear at u = ∞, then (*) admits infinitely many radial solutions, and that each of them has a different (finite) number of zeros.