In this paper, we are concerned with elliptic problems {−Δu=f(u)+g(|x|,u,x|x|⋅∇u),x∈Ω,u|∂Ω=0,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ extstyle\\begin{cases} -\\Delta u= f(u)+ g( \\vert x \\vert ,u,\\frac{x}{ \\vert x \\vert }\\cdot \ abla u),&x\\in \\Omega , \\\\ u|_{\\partial \\Omega}=0, \\end{cases} $$\\end{document} where Omega ={xin mathbb{R}^{N}:R_{1}<|x|<R_{2}} is an annular domain, N>2, 0< R_{1}<R_{2}<infty , 4(R_{2}-R_{1})(N-1)leq R_{1}. f:mathbb{R} to mathbb{R} is continuous and satisfies lim_{|xi |to infty}frac{f(xi )}{xi}=infty . g:[R_{1},R_{2}] times mathbb{R}^{2}to mathbb{R} is continuous, |g(r,xi _{0}, xi _{1})|leq C+beta |xi _{0}| for some C>0, 0<beta < frac{1}{4(R_{2}-R_{1})^{2}}. We obtain infinitely many radial solutions with prescribed nodal properties using bifurcation techniques.