Positive solutions for nonlinear Schrödinger equations with deepening potential well
Zhengping Wang, Huan-Song Zhou (2009)
Journal of the European Mathematical Society
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Displaying similar documents to “Semiclassical states for weakly coupled nonlinear Schrödinger systems”
Positive solutions for nonlinear Schrödinger equations with deepening potential well
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
Filip Ficek (2023)
Archivum Mathematicum
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Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials. ...
A Survey on Systems of Nonlinear Schrödinger Equations
Antonio Ambrosetti (2008)
Bollettino dell'Unione Matematica Italiana
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We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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A multiplicity result for the Schrodinger-Maxwell equations with negative potential
Giuseppe Maria Coclite (2002)
Annales Polonici Mathematici
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We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.
Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations.
Merle, Frank (1998)
Documenta Mathematica
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Classical Solutions of Nonlinear Schrödinger Equations.
Nakao Hayashi (1986)
Manuscripta mathematica
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On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
N. Hayashi, K. Nakamitsu, M. Tsutsumi (1986)
Mathematische Zeitschrift
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Numerical approximation of the weakly damped nonlinear Schrödinger equation.
Ciegis, R., Pakeniene, V. (2001)
Computational Methods in Applied Mathematics
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Numerical study of self-focusing solutions to the Schrödinger-Debye system
Christophe Besse, Brigitte Bidégaray (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this article we implement different numerical schemes to simulate the Schrödinger-Debye equations that occur in nonlinear optics. Since the existence of blow-up solutions is an open problem, we try to compute such solutions. The convergence of the methods is proved and simulations seem indeed to show that for at least small delays self-focusing solutions may exist.
Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.
Nakao Hayashi, Masayoshi Tsutsumi (1981)
Mathematische Zeitschrift
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Time Dependent Nonlinear Schrödinger Equations.
Wolf von Wahl, Hartmut Pecher (1979)
Manuscripta mathematica
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