Multiple Solutions for an Asymptotically Linear Problem in R^N

We consider a semilinear problem of the type Lu = f(b; u) in L2(R^N), where f(b,u)=bu as u → 0 and f(b,u)=b∞ u as |u| → ∞ (b<b∞ ). We assume that the essential spectrum of L is bounded below by a number greater than b∞ and that there exist a finite number of eigenvalues between b and b∞ . We prove existence and multiplicity results for nontrivial solutions under suitable assumptions on g. We give an application to the Schrodinger equation.