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Solutions of Nonlinear Schrӧdinger Systems

Zhijie Chen (Autor)

Buch | Softcover

XI, 180 Seiten

2016 | Softcover reprint of the original 1st ed. 2015
Springer Berlin (Verlag)
978-3-662-51542-6 (ISBN)

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The existence and qualitative properties of nontrivial solutions for some important nonlinear Schrödinger 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 Schrödinger 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.

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 Schrödinger system with critical exponent.

Erscheinungsdatum	03.08.2016
Reihe/Serie	Springer Theses
Zusatzinfo	XI, 180 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Bose-Einstein condensates • Differential calculus and equations • ground state solutions • Mathematical Applications in the Physical Sciences • Mathematical Modelling • Mathematical Physics • mathematics and statistics • nonlinear schrodinger system • Partial differential equations • Sign-changing solutions • subcritical • variational methods
ISBN-10	3-662-51542-3 / 3662515423
ISBN-13	978-3-662-51542-6 / 9783662515426
Zustand	Neuware