The existence of multiple solutions for a Ginzburg-Landau type model of superconductivity. (English) Zbl 0880.34023

The authors 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. It is shown 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.


34B15 Nonlinear boundary value problems for ordinary differential equations
78A99 General topics in optics and electromagnetic theory
Full Text: DOI


[1] DOI: 10.1137/0152034 · Zbl 0758.35075
[2] DOI: 10.1007/BF01396308 · Zbl 0516.65073
[3] DOI: 10.1063/1.1705166
[4] Yang, Proc. Roy. Soc. Edin. 114A pp 355– (1990) · Zbl 0708.35074
[5] Yang, J. Math. Phy. 31 pp 5– (1990)
[6] Kwong, J. Differential and Integral Equations 8 pp 1395– (1995)
[7] DOI: 10.1137/1034114 · Zbl 0769.73068
[8] DOI: 10.1103/RevModPhys.36.294
[9] Ginzburg, Zh. Eksperim. i. Theor. Fiz. 20 pp 1064– (1950)
[10] Bolley, Rigorous results on G.L. models in a film submitted to an exterior parallel magnetic field (1993)
[11] Bolley, Ann. Inst. Henri Poincar?, Phys. Th?orique 58 pp 189– (1993)
[12] Bolley, Methods Mathematiques et Analyse Numerique 26 pp 235– (1992)
[13] Bolley, Rigorous results for the G.L. equations associated to a superconducting film in the weak k limit. Reviews in Math. Physics 8 pp 43– (1996) · Zbl 0864.35097
[14] Abrikosov, Fundamentals of the Theory of Metals (1988)
[15] Abrikosov, Zh. Eksperim. i Teor. Fiz. 32 pp 1442– (1957)
[16] Seydel, From equilibrium to chaos; Practical bifurcation and stability analysis. (1988) · Zbl 0652.34059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.