A nonlinear superposition principle and multibump solutions of periodic Schrodinger equations

In an abstract setting we prove a nonlinear superposition principle for zeros of equivariant vector fields that are asymptotically additive in a well-defined sense. This result is used to obtain multibump solutions for two basic types of periodic stationary Schrodinger equations with superlinear nonlinearity. The nonlinear term may be of convolution type. If the superquadratic term in the energy functional is convex, our results also apply in certain cases if 0 is in a gap of the spectrum of the Schrodinger operator. (C) 2005 Elsevier Inc. All rights reserved.