This paper deals with the study of the existence and multiplicity of radial solutions for the problem -Δu(x)=f(u(x)) when x∈Ω and u(x)=0 when x∈∂Ω, where Ω={x∈R^N; a <|x| < b} with 0 < a < b is an annulus in R^N and f : R→R is a continuous function. We use as main tools Schaeffer's fixed point theorem and Leggett-Williams fixed point theorem in order to obtain radial solutions for the above problem.