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000724558 019__ $$a900397138
000724558 020__ $$a9783662454787$$qelectronic book
000724558 020__ $$a3662454785$$qelectronic book
000724558 020__ $$z9783662454770
000724558 0247_ $$a10.1007/978-3-662-45478-7$$2doi
000724558 035__ $$aSP(OCoLC)ocn897115899
000724558 035__ $$aSP(OCoLC)897115899$$z(OCoLC)900397138
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000724558 049__ $$aISEA
000724558 050_4 $$aQC174.26.W28
000724558 08204 $$a530.12/4$$223
000724558 1001_ $$aChen, Zhijie,$$eauthor.
000724558 24510 $$aSolutions of nonlinear Schrödinger systems$$h[electronic resource] /$$cZhijie Chen.
000724558 264_1 $$aHeidelberg :$$bSpringer,$$c2015.
000724558 300__ $$a1 online resource.
000724558 336__ $$atext$$btxt$$2rdacontent
000724558 337__ $$acomputer$$bc$$2rdamedia
000724558 338__ $$aonline resource$$bcr$$2rdacarrier
000724558 347__ $$atext file$$bPDF$$2rda
000724558 4901_ $$aSpringer theses
000724558 504__ $$aIncludes bibliographical references and index.
000724558 5050_ $$aIntroduction -- A BEC system with dimensions N = 2;3: Ground state solutions -- A BEC system with dimensions N = 2;3: Sign-changing solutions -- A BEC system with dimensions N = 4: Critical case -- A generalized BEC system with critical exponents in dimensions -- A linearly coupled Schr{u04E7}dinger system with critical exponent.
000724558 506__ $$aAccess limited to authorized users.
000724558 520__ $$aThe existence and qualitative properties of nontrivial solutions for some important nonlinear Schrℓʹdinger systems have been studied in this thesis. For a well-known system arising from nonlinear optics and Bose-Einstein condensates (BEC), in the subcritical case, qualitative properties of ground state solutions, including an optimal parameter range for the existence, the uniqueness and asymptotic behaviors, have been investigated and the results could firstly partially answer open questions raised by Ambrosetti, Colorado and Sirakov. In the critical case, a systematical research on ground state solutions, including the existence, the nonexistence, the uniqueness and the phase separation phenomena of the limit profile has been presented, which seems to be the first contribution for BEC in the critical case. Furthermore, some quite different phenomena were also studied in a more general critical system. For the classical Brezis-Nirenberg critical exponent problem, the sharp energy estimate of least energy solutions in a ball has been investigated in this study. Finally, for Ambrosetti type linearly coupled Schrℓʹdinger equations with critical exponent, an optimal result on the existence and nonexistence of ground state solutions for different coupling constants was also obtained in this thesis. These results have many applications in Physics and PDEs.
000724558 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed February 18, 2015).
000724558 650_0 $$aSchrödinger equation.
000724558 650_0 $$aDifferential equations, Nonlinear.
000724558 650_0 $$aBose-Einstein condensation$$xMathematical models.
000724558 77608 $$iPrint version:$$z9783662454770
000724558 830_0 $$aSpringer theses.
000724558 852__ $$bebk
000724558 85640 $$3SpringerLink$$uhttps://univsouthin.idm.oclc.org/login?url=http://link.springer.com/10.1007/978-3-662-45478-7$$zOnline Access$$91397441.1
000724558 909CO $$ooai:library.usi.edu:724558$$pGLOBAL_SET
000724558 980__ $$aEBOOK
000724558 980__ $$aBIB
000724558 982__ $$aEbook
000724558 983__ $$aOnline
000724558 994__ $$a92$$bISE