Solutions of Nonlinear Schrӧdinger Systems

Nonfiction, Science & Nature, Mathematics, Differential Equations, Applied
Cover of the book Solutions of Nonlinear Schrӧdinger Systems by Zhijie Chen, Springer Berlin Heidelberg
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Zhijie Chen ISBN: 9783662454787
Publisher: Springer Berlin Heidelberg Publication: November 24, 2014
Imprint: Springer Language: English
Author: Zhijie Chen
ISBN: 9783662454787
Publisher: Springer Berlin Heidelberg
Publication: November 24, 2014
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Berlin Heidelberg

Cover of the book Introduction to Thermoelectricity by Zhijie Chen
Cover of the book Fallsammlung zum Gesellschaftsrecht by Zhijie Chen
Cover of the book Chemical Evolution of Galaxies by Zhijie Chen
Cover of the book Dienstübergabe in der Pflege by Zhijie Chen
Cover of the book Content Analysis of Verbal Behavior by Zhijie Chen
Cover of the book Friction Material Composites by Zhijie Chen
Cover of the book Structure and Function of the Bladder Neck by Zhijie Chen
Cover of the book Clinical Ophthalmic Oncology by Zhijie Chen
Cover of the book Chromium -VI Reagents: Synthetic Applications by Zhijie Chen
Cover of the book Lip Cancer by Zhijie Chen
Cover of the book Lymphocyte Hybridomas by Zhijie Chen
Cover of the book 100 Clavicula-Pseudarthrosen by Zhijie Chen
Cover of the book Piezo-Active Composites by Zhijie Chen
Cover of the book Neonatal Intensive Care by Zhijie Chen
Cover of the book On the Centre of Gravity of the Human Body by Zhijie Chen
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy