A nonlinear superposition principle and multibump solutions of periodic Schrödinger equations |
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Authors: | Nils Ackermann |
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Institution: | School of Mathematics and Statistics F07, University of Sydney, NSW 2006, Australia |
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Abstract: | 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 Schrödinger 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 Schrödinger operator. |
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Keywords: | Stationary nonlinear Schrö dinger equation Multibump solutions Periodic potential |
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