Solutions of nonlinear Schrödinger systems [electronic resource] / Zhijie Chen.
Chen, Zhijie, author.
2015
QC174.26.W28
Available Online

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Title Solutions of nonlinear Schrödinger systems [electronic resource] / Zhijie Chen.
Author Chen, Zhijie, author.
ISBN 9783662454787 electronic book
3662454785 electronic book
9783662454770
DOI https://doi.org/10.1007/978-3-662-45478-7
Published Heidelberg : Springer, 2015.
Language English
Description 1 online resource.
Item Number 10.1007/978-3-662-45478-7 doi
Call Number QC174.26.W28
Dewey Decimal Classification 530.12/4
Summary The existence and qualitative properties of nontrivial solutions for some important nonlinear Schrℓʹdinger 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 Schrℓʹdinger 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.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Digital File Characteristics text file PDF
Source of Description Online resource; title from PDF title page (SpringerLink, viewed February 18, 2015).
Series Springer theses.
Available in Other Form Print version: 9783662454770
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Introduction
A BEC system with dimensions N = 2;3: Ground state solutions
A BEC system with dimensions N = 2;3: Sign-changing solutions
A BEC system with dimensions N = 4: Critical case
A generalized BEC system with critical exponents in dimensions
A linearly coupled Schr{u04E7}dinger system with critical exponent.

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