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Positive Solutions for the Discrete Nonlinear Schrödinger Equation: A Priori Estimates and Convergence

Verbitsky, Anton

Abstract:
We consider the discrete nonlinear stationary Schrödinger equation on a bounded n-dimensional box and on the whole space. In the first case we derive the existence of a positive classical solution of the corresponding continuous problem from a uniform a priori bound on positive discrete solutions for a general right hand side. In the second case we derive a uniform a priori bound on positive discrete solutions for the Schrödinger-type nonlinearity.

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DOI: 10.5445/IR/1000043829
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Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Hochschulschrift
Jahr 2014
Sprache Englisch
Identifikator urn:nbn:de:swb:90-438295
KITopen-ID: 1000043829
Verlag KIT, Karlsruhe
Abschlussart Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Analysis (IANA)
Prüfungsdaten 25.06.2014
Referent/Betreuer Prof. W. Reichel
KIT – Die Forschungsuniversität in der Helmholtz-Gemeinschaft
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