Segregated vector Solutions for nonlinear Schrödinger systems with electromagnetic potentials
Author(s) -
Jing Yang
Publication year - 2017
Publication title -
communications on pure andamp applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2017087
Subject(s) - nabla symbol , physics , bounded function , lambda , coupling (piping) , coupling constant , nonlinear system , combinatorics , mathematical physics , mathematical analysis , quantum mechanics , omega , mathematics , mechanical engineering , engineering
In this paper, we study the following nonlinear Schrodinger system in \begin{document}$\mathbb{R}^3$\end{document} \begin{document}$\left\{ \begin{array}{*{35}{l}} {{(\frac{\nabla }{i}-A(y))}^{2}}u+{{\lambda }_{1}}(|y|)u=|u{{|}^{2}}u+\beta |v{{|}^{2}}u,x'>where \begin{document}$A(y)=A(|y|)∈ C^1(\mathbb{R}^3,\mathbb{R})$\end{document} is bounded, \begin{document}$λ_1(|y|),λ_2(|y|)$\end{document} are continuous positive radial potentials, and \begin{document}$β∈ \mathbb{R}$\end{document} is a coupling constant. We proved that if \begin{document}$A(y),λ_1(y),λ_2(y)$\end{document} satisfy some suitable conditions, the above problem has infinitely many non-radial segregated solutions.
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