Solutions of nonlinear Schrӧdinger systems [Documento eletrónico] / Zhijie Chen
Language: eng.Country: Germany.Publication: Berlin, Heidelberg : Springer , 2015Description: XI, 180 p.ISBN: 978-3-662-45478-7.Series: Springer Theses Recognizing Outstanding Ph.D. ResearchSubject - Topical Name: 3647Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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QA374.SPR FCT 96467 Hamiltonian partial differential equations and applications | QA374.SPR FCT 96472 Evolution equations of von Karman type | QA374.SPR FCT 96539 Applied partial differential equations | QA374.SPR FCT 96587 Solutions of nonlinear Schrӧdinger systems | QA374.SPR FCT 96654 An introduction to viscosity solutions for fully nonlinear PDE with applications to calculus of variations in L∞ | QA374.SPR FCT 96714 Evolution PDEs with nonstandard growth conditions, existence, uniqueness, localization, blow-up | QA374.SPR FCT 96734 From particle systems to partial differential equations II, particle systems and PDEs II, Braga, Portugal, December 2013 |
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The existence and qualitative properties of nontrivial solutions for some important nonlinear Schrӧdinger systems have been studied in this thesis. For a well-known system arising from nonlinear optics and Bose-Einstein condensates (BEC), in the subcritical case, qualitative properties of ground state solutions, including an optimal parameter range for the existence, the uniqueness and asymptotic behaviors, have been investigated and the results could firstly partially answer open questions raised by Ambrosetti, Colorado and Sirakov. In the critical case, a systematical research on ground state solutions, including the existence, the nonexistence, the uniqueness and the phase separation phenomena of the limit profile has been presented, which seems to be the first contribution for BEC in the critical case. Furthermore, some quite different phenomena were also studied in a more general critical system. For the classical Brezis-Nirenberg critical exponent problem, the sharp energy estimate of least energy solutions in a ball has been investigated in this study. Finally, for Ambrosetti type linearly coupled Schrӧdinger equations with critical exponent, an optimal result on the existence and nonexistence of ground state solutions for different coupling constants was also obtained in this thesis. These results have many applications in Physics and PDEs.
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