Semi-Classical Bound States for Schrodinger Equations with Potentials Vanishing or Unbounded at Infinity

In this paper we study the existence and qualitative property of standing wave solutions [image omitted] for the nonlinear Schrodinger equation [image omitted]. Let [image omitted]. For any integer k epsilon 1, we prove existence of standing wave solutions with u0 having k local maximum points and concentrating near a given local maximum point of when epsilon is small. The potentials V and K are allowed to be either vanishing or unbounded at infinity. Existence of solutions concentrating near k distinct non-degenerate critical points of has been proved under the same assumptions on V and K as well.