Existence of multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations with potentials vanishing at infinity

Abstract

For a singularly perturbed nonlinear elliptic equation, epsilon(2)Delta u - V(x)u + u(p) = 0, x is an element of R(N), there are solutions concentrating around critical points of V with different energy scales with respect to small epsilon > 0. We combine the solutions when lim inf(vertical bar x vertical bar ->infinity) vertical bar x vertical bar(2)V(x) > 0.