Multiple solutions for an asymptotically linear problem in RN

We consider a semilinear problem of the type Lu = f (b, u) in L-2 (R-N), where f (b, u) similar or equal to bu as u --> 0 and f (b, u) similar or equal to b(infinity)u as \u\ --> infinity (b < b(infinity)). We assume that the essential spectrum of L is bounded below by a number greater than b(infinity) and that there exist a finite number of eigenvalues between b and b(infinity). We prove existence and multiplicity results for nontrivial solutions under suitable assumptions on g. We give an application to the Schrodinger equation. (C) 2003 Elsevier Ltd. All rights reserved.