Solution set splitting at low energy levels in Schrodinger equations with periodic and symmetric potential

摘要

The time-independent superlinear Schrodinger equation with spatially periodic and positive potential admits sign-changing two-bump solutions if the set of positive solutions at the minimal nontrivial energy level is the disjoint union of period translates of a compact set. Assuming a reflection symmetric potential we give a condition on the equation that ensures this splitting property for the solution set. Moreover, we provide a recipe to explicitly verify the condition, and we carry out the calculation in dimension one for a specific class of potentials. (C) 2008 Elsevier Inc. All rights reserved.