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.


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