Positive radial solutions for elliptic equations with sign-changing nonlinear terms in an annulus

This paper deals with the existence and nonexistence of positive radial solutions of the elliptic equation {-Delta u = f (|x|, u), u is an element of Omega, u|(partial derivative Omega) = 0, where Omega = {x is an element of R-N : r(1) < |x| < r(2)}, N >= 3 and f is an element of C([r(1), r(2)] x R+), whose sign may change. We present new eigenvalue criteria for the existence and nonexistence to this problem. The discussion is based on the fixed point index theory in cones.