Solutions of Nonlinear Schrӧdinger Systems

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 sta...

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Tác giả chính:	Chen, Zhijie
Định dạng:	Sách
Ngôn ngữ:	English
Được phát hành:	Springer 2015
Những chủ đề:	Mathematical models Einstein condensation Bose Nonlinear Differential equations Schrödinger equation
Truy cập trực tuyến:	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58337
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id	oai:scholar.dlu.edu.vn:DLU123456789-58337
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spelling	oai:scholar.dlu.edu.vn:DLU123456789-583372023-11-11T06:07:00Z Solutions of Nonlinear Schrӧdinger Systems Chen, Zhijie Mathematical models Einstein condensation Bose Nonlinear Differential equations Schrödinger equation 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. 2015-09-17T02:58:12Z 2015-09-17T02:58:12Z 2015 Book 978-3-662-45478-7 978-3-662-45477-0 https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58337 en application/pdf Springer
institution	Thư viện Trường Đại học Đà Lạt
collection	Thư viện số
language	English
topic	Mathematical models Einstein condensation Bose Nonlinear Differential equations Schrödinger equation
spellingShingle	Mathematical models Einstein condensation Bose Nonlinear Differential equations Schrödinger equation Chen, Zhijie Solutions of Nonlinear Schrӧdinger Systems
description	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.
format	Book
author	Chen, Zhijie
author_facet	Chen, Zhijie
author_sort	Chen, Zhijie
title	Solutions of Nonlinear Schrӧdinger Systems
title_short	Solutions of Nonlinear Schrӧdinger Systems
title_full	Solutions of Nonlinear Schrӧdinger Systems
title_fullStr	Solutions of Nonlinear Schrӧdinger Systems
title_full_unstemmed	Solutions of Nonlinear Schrӧdinger Systems
title_sort	solutions of nonlinear schrӧdinger systems
publisher	Springer
publishDate	2015
url	https://scholar.dlu.edu.vn/thuvienso/handle/DLU123456789/58337
_version_	1782534045791420416

Solutions of Nonlinear Schrӧdinger Systems

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