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An abstract approach to multibump solutions of periodic Schrödinger equations and applications. (English) Zbl 1224.35112

Summary: We review a recent result on nonlinear superposition of zeros of asymptotically additive equivariant vector fields. As application we present existence results for multibump solutions of nonlinear periodic Schrödinger equations. Here 0 may be in a gap of the spectrum of the Schrödinger operator, and the nonlinearity may be of convolution type.

MSC:

35J60 Nonlinear elliptic equations
35B10 Periodic solutions to PDEs
47J30 Variational methods involving nonlinear operators
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