Multiple positive normalized solutions for nonlinear Schrödinger systems

We consider the existence of multiple positive solutions to the nonlinear Schrödinger systems set on , under the constraint Here are prescribed, , and the frequencies are unknown and will appear as Lagrange multipliers. Two cases are studied, the first when , the second when In both cases, assuming...

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Bibliographic Details
Published inNonlinearity Vol. 31; no. 5; pp. 2319 - 2345
Main Authors Gou, Tianxiang, Jeanjean, Louis
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.05.2018
Subjects
Analysis of PDEs
Mathematics
nonlinear Schrödinger systems
normalized solutions
solitary waves
variational methods
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Summary:We consider the existence of multiple positive solutions to the nonlinear Schrödinger systems set on , under the constraint Here are prescribed, , and the frequencies are unknown and will appear as Lagrange multipliers. Two cases are studied, the first when , the second when In both cases, assuming that is sufficiently small, we prove the existence of two positive solutions. The first one is a local minimizer for which we establish the compactness of the minimizing sequences and also discuss the orbital stability of the associated standing waves. The second solution is obtained through a constrained mountain pass and a constrained linking respectively.
Bibliography:NON-102379.R1
London Mathematical Society
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aab0bf