Construction of the Leray-Schauder degree for elliptic operators in unbounded domains

A. I. Volpert; V. A. Volpert

Annales de l'I.H.P. Analyse non linéaire (1994)

  • Volume: 11, Issue: 3, page 245-273
  • ISSN: 0294-1449

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Volpert, A. I., and Volpert, V. A.. "Construction of the Leray-Schauder degree for elliptic operators in unbounded domains." Annales de l'I.H.P. Analyse non linéaire 11.3 (1994): 245-273. <http://eudml.org/doc/78331>.

@article{Volpert1994,
author = {Volpert, A. I., Volpert, V. A.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {quasilinear elliptic operators in unbounded domains; Leray-Schauder degree},
language = {eng},
number = {3},
pages = {245-273},
publisher = {Gauthier-Villars},
title = {Construction of the Leray-Schauder degree for elliptic operators in unbounded domains},
url = {http://eudml.org/doc/78331},
volume = {11},
year = {1994},
}

TY - JOUR
AU - Volpert, A. I.
AU - Volpert, V. A.
TI - Construction of the Leray-Schauder degree for elliptic operators in unbounded domains
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1994
PB - Gauthier-Villars
VL - 11
IS - 3
SP - 245
EP - 273
LA - eng
KW - quasilinear elliptic operators in unbounded domains; Leray-Schauder degree
UR - http://eudml.org/doc/78331
ER -

References

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  1. [1] M.A. Krasnoselskii and P.P. Zabreiko, Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin, New York, 1984. Zbl0546.47030MR736839
  2. [2] A.I. Volpert and V.A. Volpert, Construction of the Rotation of the Vector Field for Operators Describing Wave Solutions of Parabolic Systems, Soviet Math. Dokl., Vol. 36, 1988, n° 3, pp. 452-455. Zbl0704.35067MR919249
  3. [3] A.I. Volpert and V.A. Volpert, Application of the Rotation Theory of Vector Fields to the Study of Wave Solutions of Parabolic Equations, Trans. Moscow Math. Soc., Vol. 52, 1990, pp. 59-108. Zbl0711.35064
  4. [4] I.V. Skrypnik, Nonlinear Elliptic Equations of Higher Order, Naukova Dumka, Kiev, 1973 (in Russian). Nonlinear elliptic boundary value problems. Teubner-Texte zur Mathematik, Vol. 91, 1986, BSB B.G. Teubner Verlagsgesellschaft, Leipzig, 232 p. Zbl0617.35001
  5. [5] V.A. Volpert and A.I. Volpert, Travelling Waves Described by Monotone Parabolic Systems, Preprint n° 146, CNRS URA740, 1993, 46 p. 
  6. [6] H. Berestycki and L. Nirenberg, Travelling Fronts in Cylinder, Annales de l'IHP. Analyse non linéaire, Vol. 9, 1992, n° 5, pp. 497-572. Zbl0799.35073MR1191008
  7. [7] R. Gardner, Existence of Multidimensional Travelling Wave Solutions of an Initial-Boundary value Problem, J. Diff. Eqns, Vol. 61, 1986, pp. 335-379. Zbl0549.35066MR829368
  8. [8] S. Heinze, Travelling Waves for Semilinear Parabolic Partial Differential Equations in Cyclindrical domains, Preprint n° 506, Heidelberg, 1989, 46 p. 
  9. [9] O.A. Ladyzhenskaya and N.N. Uraltseva, Linear and quasilinear elliptic equations, Academic Press, New York, 1968. Zbl0164.13002MR244627
  10. [10] M. Escobedo and O. Kavian, Variational Problems Related to Self-similar Solutions of the Heat Equation, Nonlinear Analysis TMA, Vol. 11, 1987, n° 10, pp. 1103-1133. Zbl0639.35038MR913672
  11. [11] D. Henry, Geometrical Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin, New York, 1981. Zbl0456.35001MR610244
  12. [12] A.I. Volpert and S.I. Hudjaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics, Martinus Nijhoff Publisher, 1985. Zbl0564.46025MR785938
  13. [13] F.E. Browder, Degree Theory for Nonlinear Mappings, Proceedings of Symposia in Pure Mathematics, Vol. 45, 1986, Part 1, pp. 203-226. Zbl0601.47050MR843560

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