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Existence and non-existence of solutions to the Ginzburg-Landau equations in a semi-infinite superconducting film

Author(s): Y. Almog
Journal: Quart. Appl. Math. 63 (2005), 1-12.
MSC (2000): Primary 82D55
Posted: December 14, 2004
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Abstract: For the problem
\begin{gather*}\frac{\psi^{\prime \prime}}{\kappa^2} = \psi^{3} - \psi + A^{2}\p... ...ime}(0)= \psi(\infty)=0, A^{\prime}(0)=A^{\prime}(\infty)=h , \end{gather*}
it is proved for type II superconductors ( $\kappa>1/\sqrt{2}$) that

1.
No solutions can exist for $h \leq 1/\sqrt{2}$ other than the normal state $\psi\equiv0$, $A=hx+C$;
2.
Positive solutions ($\psi>0$) exist whenever $1/\sqrt{2}<h<h_{c_3}\approx1.7\kappa$;
3.
As $h \downarrow 1/\sqrt{2}$, the limit of any converging subsequence satisfies $A=0, \; \psi=1$ at infinity.

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Additional Information:

Y. Almog
Affiliation: Faculty of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

PII: S0033-569X-04-00943-7
Received by editor(s): January 21, 2003
Posted: December 14, 2004
Copyright of article: Copyright 2004, Brown University


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