Oriented degree of Fredholm maps of non-negative index and its application to global bifurcation of solutions

  • V. G. Zvyagin
  • N. M. Ratiner
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1520)


Normal Bundle Banach Manifold Nonlinear Elliptic Boundary Continuous Perturbation Oriented Degree 
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  1. 1.
    Elworthy K.D., Tromba A.J. Differential structures and Fredholm maps on Banach manifolds // Proc. Sympos. Pure Math. (Global Analysis).-1970. v.15-p.45–74.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Sapronov Yu.I. On the dergree theory for nonlinear Fredholm maps // Trudy NII matematiki VGU.-Voronezh, 1973, No II, p.93–101 (in Russian).Google Scholar
  3. 3.
    Zvyagin V. G. Investigation of topological characteristics of nonlinear operators. PhD. Thesis, Voronezh, 1974 (in Russian).Google Scholar
  4. 4.
    Zvyagin V.G. On the existence of a continuous branch of eigen-values for nonlinear elliptic boundary value problem // Diff. equations, 1977, vol.13, No 8, p.1524–1527 (in Russian).Google Scholar
  5. 5.
    Ratiner N.M. On the degree theory for Fredholm mappings of manifolds // Equations on Manifolds. Voronezh, 1982, p.126–129 (in Russian).zbMATHGoogle Scholar
  6. 6.
    Borisovich Yu.G., Zvyagin V.G., Sapronov Yu.I. Nonlinear Fredholm maps and Leray-Schauder theory // Uspekhi Mat. Nauk (Russian Math. Surveys), 1977, vol.32, No 4, p, 3–54.zbMATHGoogle Scholar
  7. 7.
    Zvyagin V. G., Ratiner N.M. The degree of completely continuous perturbations of Fredholm maps and its application to bifurcation of solutions // Dokl. AN Ukr. SSR, 1989, No 6, p.8–11 (in Russian).Google Scholar
  8. 8.
    Rabinowitz P.H. A global theorem for non-linear eigenvalue problems and applications // Contrib. Nonlinear Fcl Anal. Academic Press.-1971, p. 11–36.Google Scholar
  9. 9.
    Zvyagin V.G. On the structure of the set of solutions of a nonlinear eiliptic problem with fixed boundary conditions // Global Analysis Studies and Applications, IV. Springer-Veriag, 1990 (Lect. Notes in Mathematics, vol. 1400).Google Scholar
  10. 10.
    Nirenberg L. Topics in non-linear functional analysis. New York, 1974.Google Scholar
  11. 11.
    Pontryagin L.S. Smooth manifolds and their applications in homotopy theory. Moscow, 1976 (in Russin).Google Scholar
  12. 12.
    Husemoller D. Fibre bundies. McGraw Hill, 1966.Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • V. G. Zvyagin
    • 1
  • N. M. Ratiner
    • 1
  1. 1.Department of MathematicsVoronezh State UniversityVoronezhUSSR

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