Stable Solutions with Zeros to the Ginzburg–Landau Equation with Neumann Boundary Condition

This paper is devoted to the Ginzburg–Landau equationΔΦ+λ(1−|Φ|2)Φ=0,Φ=u1+iu2in a bounded domainΩ⊂Rnwith the homogeneous Neumann boundary condition. The previous works [12–14] showed that for largeλthere exist stable non-constant solutions with no zeros in domains, which are topologically non-trivia...

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Bibliographic Details
Published in:Journal of Differential Equations 1996-07, Vol.128 (2), p.596-613
Main Authors: Jimbo, Shuichi, Morita, Yoshihisa
Format: Article
Language:English
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Summary:This paper is devoted to the Ginzburg–Landau equationΔΦ+λ(1−|Φ|2)Φ=0,Φ=u1+iu2in a bounded domainΩ⊂Rnwith the homogeneous Neumann boundary condition. The previous works [12–14] showed that for largeλthere exist stable non-constant solutions with no zeros in domains, which are topologically non-trivial in a certain sense. In this aritcle it is proved that for a domainΩcontaining a non-trivial domainDas a subset, there exist stable solutions with zeros provided that the volume ofΩ\Dis sufficiently small.
ISSN:0022-0396
1090-2732
DOI:10.1006/jdeq.1996.0107