Existence of Multi-bump Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations.

For elliptic equations of the form ε² Δu - V(x)u + up = 0, x ∈ RN, where the potential V satisfies lim inf¦x¦→∞ V(x) > infRN V(x) = 0, we prove the existence of new kinds of solutions, corresponding to semi-classical standing waves for nonlinear Schrödinger equations, with several local maximum points whose local maximum values are of different scales with respect to ε → 0. [ABSTRACT FROM AUTHOR]