Singularly perturbed elliptic problems with superlinear or asymptotically linear nonlinearities

We consider a class A equations of the form -epsilon(2) Deltau + V(x)u = f(u), u is an element of H-1(R-N). By variational methods, we show the existence of families of positive solutions concentrating around local minima of the potential V(x), as epsilon --> 0. We do not require uniqueness of the ground state solutions of the associated autonomous problems nor the monotonicity of the function xi --> f(xi)/xi. We deal with asymptotically linear as well as superlinear nonlinearities.