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The existence of multiple solutions for a Ginzburg–Landau type model of superconductivity

Published online by Cambridge University Press:  26 September 2008

S. P. Hastings ,
M. K. Kwong  and
W. C. Troy
S. P. Hastings
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, 301 Thackray Hall, Pittsburgh, PA 15260, USA
M. K. Kwong
Affiliation:
Argonne National Laboratory.
W. C. Troy
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, 301 Thackray Hall, Pittsburgh, PA 15260, USA
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Abstract

We study a system of two second-order differential equations with cubic nonlinearities which model a film of superconductor material subjected to a tangential magnetic field. We verify some recent conjectures of one of the authors about multiplicity of solutions. We show that for an appropriate range of parameter values the relevant boundary value problem has at least two symmetric solutions. It is also proved that a second range of parameters exists for which there are three symmetric solutions.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 6 , December 1996 , pp. 559 - 574
Copyright
Copyright © Cambridge University Press 1996

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References

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