Multiplicity results for sign changing bound state solutions of a semilinear equation

In this paper we give conditions on f so that the problemΔu+f(u)=0,x∈RN,N≥2, has at least two radial bound state solutions with any prescribed number of zeros, and such that u(0)u(0) belongs to a specific subinterval of (0,∞)(0,∞). This property will allow us to give conditions on f so that this problem has at least any given number of radial solutions having a prescribed number of zeros.