MULTIBUMP SOLUTIONS OF NONLINEAR PERIODIC SCHRÖDINGER EQUATIONS IN A DEGENERATE SETTING

Abstract

We prove the existence of infinitely many geometrically distinct two bump solutions of periodic superlinear Schrödinger equations of the type -Δu + V(x)u = f(x,u), where x ∈ ℝ N and lim |x| → ∞ u(x) = 0. The solutions we construct change sign and have exactly two nodal domains. The usual multibump constructions for these equations rely on strong non-degeneracy assumptions. We present a new approach that only requires a weak splitting condition. In the second part of the paper we exhibit classes of potentials V for which this splitting condition holds.