On the Number of Radially Symmetric Solutions to Dirichlet Problems with Jumping Nonlinearities of Superlinear Order

This paper is concerned with the multiplicity of radially symmetric solutions u(x) to the Dirichlet problem Δu+f(u)=h(x)+cφ(x) on the unit ball Ω⊂RN with boundary condition u=0 on ∂Ω. Here φ(x) is a positive function and f(u) is a function that is superlinear (but of subcritical growth) for large positive u, while for large negative u we have that f\u27(u)\u3cμ, where μ is the smallest positive eigenvalue for Δψ+μψ=0 in Ω with ψ=0 on ∂Ω. It is shown that, given any integer k≥0, the value c may be chosen so large that there are 2k+1 solutions with k or less interior nodes. Existence of positive solutions is excluded for large enough values of c