Infinitely many positive solutions for nonlinear equations with non-symmetric potentials

We consider the following nonlinear Schrodinger equation {Delta u - (1 + delta V)u + f(u) = 0 in R-N, u > 0 in R-N, u is an element of H-1(R-N) where is a continuous potential and is a nonlinearity satisfying some decay condition and some non-degeneracy condition, respectively. Using localized energy method, we prove that there exists a such that for , the above problem has infinitely many positive solutions. This generalizes and gives a new proof of the results by Cerami et al. (Comm. Pure Appl. Math. 66, 372-413, 2013). The new techniques allow us to establish the existence of infinitely many positive bound states for elliptic systems.