A remark on multiplicity of solutions for the Ginzburg-Landau equation

Feng Zhou; Qing Zhou

Annales de l'I.H.P. Analyse non linéaire (1999)

  • Volume: 16, Issue: 2, page 255-267
  • ISSN: 0294-1449

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Zhou, Feng, and Zhou, Qing. "A remark on multiplicity of solutions for the Ginzburg-Landau equation." Annales de l'I.H.P. Analyse non linéaire 16.2 (1999): 255-267. <http://eudml.org/doc/78465>.

@article{Zhou1999,
author = {Zhou, Feng, Zhou, Qing},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Ginzburg-Landau equation; multiple solutions; Ljusternik-Schnirelman category},
language = {eng},
number = {2},
pages = {255-267},
publisher = {Gauthier-Villars},
title = {A remark on multiplicity of solutions for the Ginzburg-Landau equation},
url = {http://eudml.org/doc/78465},
volume = {16},
year = {1999},
}

TY - JOUR
AU - Zhou, Feng
AU - Zhou, Qing
TI - A remark on multiplicity of solutions for the Ginzburg-Landau equation
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1999
PB - Gauthier-Villars
VL - 16
IS - 2
SP - 255
EP - 267
LA - eng
KW - Ginzburg-Landau equation; multiple solutions; Ljusternik-Schnirelman category
UR - http://eudml.org/doc/78465
ER -

References

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  1. [AB1] L. Almeida and F. Bethuel, Multiplicity results for the Ginzburg-Landau equation in presence of symmetries, to appear in Houston Math. J. Zbl0901.35029
  2. [AB2] L. Almeida and F. Bethuel, Méthodes topologiques pour l'équation de Ginzburg-Landau, C. R. Acad. Sci. Paris, Vol. 320, 1996, pp. 935-938. Zbl0826.35036
  3. [AB3] L. Almeida and F. Bethuel, Topological methods for the Ginzburg-Landau equations, to appear in J. Math. Pures et Appl., 1996. Zbl0904.35023
  4. [Ar] V.I. ARNOL'D, The cohomology ring of the colored braid group (English, Russian original), Math. Notes, Vol. 5, 1969, pp. 138-140 ; translation from, Mat. Zametki, Vol. 5, 1969, pp. 227-231. Zbl0277.55002MR242196
  5. [BBH1] F. Bethuel, H. Brezis and F. Hélein, Asymptotics for the minimization of a Ginzburg-Landau functional, Calc. of Vari. and PDE's, Vol. 1, 1993, pp. 123-148. Zbl0834.35014MR1261720
  6. [BBH2] F. Bethuel, H. Brezis and F. Hélein, Ginzburg-Landau Vortices, Birkhäuser, 1994. Zbl0802.35142MR1269538
  7. [BCL] H. Brezis, J.M. Coron and E.H. Lieb, Harmonic maps with defects, Comm. Math. Phys., Vol. 107, 1986, pp. 649-705. Zbl0608.58016MR868739
  8. [BG] I. Berntein and T. Ganea, Homotopical nilpotency, Illinois J. Math., Vol. 10, 1961, pp. 99-130. Zbl0096.17602MR126277
  9. [FP] P. Felmer and M. Del Pino, Local minimizers for the Ginzburg-Landau energy, Preprint. Zbl0943.35086MR1466408
  10. [Li] F.H. Lin, Solutions of Ginzburg-Landau equations and critical points of the renormalized energy, Ann. IHP, Analyse Non Linéaire, Vol. 12, 1995, pp. 599-622. Zbl0845.35052MR1353261
  11. [Pa] R.S. Palais, Ljusternik-Schnirelman theory on Banach manifolds, Topology, Vol. 5, 1966, pp. 115-132. Zbl0143.35203MR259955

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