On the multiplicity of radial solutions to superlinear Dirichlet problems in bounded domains

In this paper we are concerned with the existence and multiplicity of nodal solutions to the Dirichlet problem associated to the elliptic equation Δu+q(|x|)g(u)=0 in a ball or in an annulus in .The nonlinearity g has a superlinear and subcritical growth at infinity, while the weight function q is nonnegative in [0,1] and strictly positive in some interval [r₁,r₂]⊂[0,1].By means of a shooting approach, together with a phase-plane analysis, we are able to prove the existence of infinitely many solutions with prescribed nodal properties.