Nodal radial solutions for a superlinear problem

The superlinear Dirichlet problem -Δu=g(u)-λ-Δu=g(u)-λ is considered. Existence of Nodal radial solutions is proved for λλ large enough without the classical condition on the increasing of g(x)g(x) depending on the dimension of the space [W. Dambrosio, On the multiplicity of radial solutions to superlinear Dirichlet problems in bounded domains, J. Differential Equations 196 (2004) 91–118; D. de Figueiredo, P.L. Lions, R.D. Nussbaum, A priory estimates and existence results of positive solutions of semilinear elliptic equations, J. Math. Pures Appl. 61 (1982)]. The proof is based on a qualitative description of solutions and a new classification given in ([M. Rouaki, Topological degree and a nonlinear Dirichlet problem, Nonlinear Anal. 54 (2003) 801–817]).