Overview
- Presents the first substantial progress in the study of optimal parameter ranges for the existence of ground state solutions to the well-known BEC system in the subcritical case
- Among the first contributions to the research of the well-known BEC system in the critical case
- Gives a sharp estimate of least energy to the classical Brezis-Nirenberg problem Nominated as an outstanding PhD thesis by Tsinghua University in 2013
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Theses (Springer Theses)
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Solutions of Nonlinear Schrӧdinger Systems
Authors: Zhijie Chen
Series Title: Springer Theses
DOI: https://doi.org/10.1007/978-3-662-45478-7
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2015
Hardcover ISBN: 978-3-662-45477-0Published: 05 December 2014
Softcover ISBN: 978-3-662-51542-6Published: 23 August 2016
eBook ISBN: 978-3-662-45478-7Published: 24 November 2014
Series ISSN: 2190-5053
Series E-ISSN: 2190-5061
Edition Number: 1
Number of Pages: XI, 180
Topics: Partial Differential Equations, Mathematical Applications in the Physical Sciences, Mathematical Physics