Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations.
Merle, Frank (1998)
Documenta Mathematica
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Displaying similar documents to “Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity”
Blow-up phenomena for critical nonlinear Schrödinger and Zakharov equations.
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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.
Positive solutions for nonlinear Schrödinger equations with deepening potential well
Zhengping Wang, Huan-Song Zhou (2009)
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Classical Solutions of Nonlinear Schrödinger Equations in Higher Dimensions.
Nakao Hayashi, Masayoshi Tsutsumi (1981)
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Semiclassical states for weakly coupled nonlinear Schrödinger systems
Eugenio Montefusco, Benedetta Pellacci, Marco Squassina (2008)
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We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
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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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. ...
Nonlinear Schrödinger equation on four-dimensional compact manifolds
Patrick Gérard, Vittoria Pierfelice (2010)
Bulletin de la Société Mathématique de France
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We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness...
Classical Solutions of Nonlinear Schrödinger Equations.
Nakao Hayashi (1986)
Manuscripta mathematica
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Global existence of small classical solutions to nonlinear Schrödinger equations
Tohru Ozawa, Jian Zhai (2008)
Annales de l'I.H.P. Analyse non linéaire
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Dunkl-Schrödinger Equations with and without Quadratic Potentials
Mejjaoli, Hatem (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10. The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.