Existence of multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations

Abstract

For elliptic equations of the form epsilon2 Deltau - V(x)u + u(p) = 0, x epsilon R-N, where the potential V satisfies lim inf(\x\-->infinity) V(x) > inf(RN) V(x) = 0, we prove the existence of new kinds of solutions, corresponding to semi-classical standing waves for nonlinear Schrodinger equations, with several local maximum points whose local maximum values are of different scales with respect to epsilon --> 0.