Infinitely many radial solutions of superlinear elliptic problems with dependence on the gradient terms in an annulus

In this paper, we are concerned with elliptic problems {-Delta u = f(u) + g(|x|, u, x/|x|. del u), x is an element of Omega, u|(partial derivative Omega) =0, where Omega = {x is an element of R-N : R-1 < |x| < R-2 } is an annular domain, N > 2, 0 < R-1 < (R)2 < infinity, 4(R-2 - R-1)(N - 1) <= R-1. f : R -> R is continuous and satisfies lim(|xi|->infinity) f (xi)/xi =infinity. g : [R-1, R-2] xR(2) -> R is continuous, |g(r,xi(0),xi(1))| <= C + beta|xi(0) | for some C > 0, 0 < beta < 1/4(R-2-R-1)(2). We obtain infinitely many radial solutions with prescribed nodal properties using bifurcation techniques.