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Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations*

Published online by Cambridge University Press:  14 November 2011

Silvia Cingolani
Affiliation:
Dipartimento di Matematica, Politecnico di Bari, via E. Orabona 4, 1-70125 Bari, Italy e-mail: [email protected]
Margherita Nolasco
Affiliation:
Dipartimento di Matematica, Università di Roma ‘La Sapienza’, P.le Aldo Moro 7, 1-00185 Roma, Italy e-mail: [email protected]

Extract

For a class of nonlinear Schrodinger equations, we prove the existence of semiclassical stationary states with possibly infinitely many concentration points. As h → 0, these states concentrate near critical points of the potential. Furthermore, for periodic potential, these states can be constructed to satisfy periodic boundary conditions.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1998

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