Skip to main content
SpringerLink
Log in

Branching of solutions of smooth Fredholm equations

  • Conference paper
  • First Online:
Global Analysis — Studies and Applications I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1108))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Krasnosel'sky, M.A. Topological Methods in the Theory of Nonlinear Integral Equations, Gostekhizdat, Moscow, 1956.

    Google Scholar 

  2. Wainberg, M.M. and Trenogin, V.A. Lyapunov-Schmidt Methods in the Theory of Nonlinear Equations and Their Further Development, Uspehi Math. Nauk, 1962, vol. 17, issue 2.

    Google Scholar 

  3. Arnold, V.I. Singularities of Smooth Mappings, Uspehi Math. Nauk, 1968, vol. 23, issue 1.

    Google Scholar 

  4. Thom, R. and Levine, H. Singularities of Differentiable Mappings, I.-Bonn, 1959.

    Google Scholar 

  5. Malgrange, B. Ideals of Differentiable Functions, Oxford University Press, 1966.

    Google Scholar 

  6. Wainberg, M.M. and Trenogin, V.A. Branching Theory of Solutions of Nonlinear Equations, Nauka, Moscow, 1969.

    Google Scholar 

  7. Krasnosel'sky, M.A., Vainikko, G.M., Zabreiko, P.P., Rutitsky, Ya.B., and Stetsenko, V.Ya. Approximate Solution of Operator Equations, Nauka, Moscow, 1969.

    Google Scholar 

  8. Pham, F. Introduction a l'etude topologique des singularites de Landau, Gauthier-Villars, Paris, 1967.

    MATH  Google Scholar 

  9. Milnor, J. Singular Points of Complex Hypersurfaces, Annals of Math. Studies 61, Princeton University Press, New Jersey, 1968.

    MATH  Google Scholar 

  10. Palamodov, V.P. Remarks on Finite-to-One Differentiable Mappings, Functional Analysis, 1972, vol. 6, issue 2.

    Google Scholar 

  11. Arnold, V.I. Lectures on Bifurcations and Versal Families, Uspehi Math. Nauk, 1972, vol. 27, issue 5.

    Google Scholar 

  12. Bifurcation Theory and Nonlinear Eigenvalue Problems. Eds. J.B. Keller and S. Antman, W.A. Benjamin, Inc., New York-Amsterdam, 1969.

    Google Scholar 

  13. Shoshitaishvili, A.N. Structures of Ideals of Local Rings of Finite-to-One Mappings of Spaces with Equal Dimensions is Self-dual, Uspehi Math. Nauk, 1974, vol. 29, issue 3.

    Google Scholar 

  14. Kushnirenko, A.I. Newton Polyhedrons and Milnor Numbers, Functional Analysis, 1975, vol. 9, issue 1.

    Google Scholar 

  15. Botashev, A.I. Finite Methods in the Theory or Mutivariate Branching, Frunze, 1976.

    Google Scholar 

  16. Varchenko, A.N. Newton Polyhedrons and Estimates of Oscillating Integrals, Functional Analysis, 1976, vol. 10, issue 3.

    Google Scholar 

  17. Brecker, Th. and Lander, L. Differentiable Germs and Catastrophes, London Mathematical Society Lecture Notes 17, Cambridge, 1975.

    Google Scholar 

  18. Nirenberg, L. Topics in Nonlinear Functional Analysis, Courant Inst. of Math. Sci., New York, 1974.

    MATH  Google Scholar 

  19. Khimshiashvili, G.N. On Local Degree of a Smooth Mapping, Soobshch. AN GSSR, 1977, vol. 85, N 2.

    Google Scholar 

  20. Khimshiashvili, G.N. On Small Solutions of Nonlinear Fredholm Equations, Vestn. Moscow State University, ser. math. mech., 1977, N 2.

    Google Scholar 

  21. Golubitsky, M. and Guillemin, V. Stable Mappings and Their Singularities, Graduate Texts in Mathematics 14, Springer-Verlag, New York-Heidelberg-Berlin, 1973.

    MATH  Google Scholar 

  22. Borisovich, Yu.G., Zvyagin, V.G., and Sapronov, Yu.I. Nonlinear Fredholm Mappings and the Leray-Schauder Theory, Uspehi Math. Nauk, 1977, vol. 32, issue 4.

    Google Scholar 

  23. Zachepa, V.R. On Extension Along Parameter of Regularly Branching Solutions of Nonlinear Operator Equations, In: Methods of Solving Operator Equations, Voronezh University Press, Voronezh, 1978.

    Google Scholar 

  24. Bliznyakov, N.M. On Estimates of Topological Index of a Singular Point of Vector Field, Dep. in VINITI on Feb. 8, 1979, No. 589-79.

    Google Scholar 

  25. Arnold, V.I. Additional Chapters on the Theory of Differential Equations, Nauka, Moscow, 1978.

    Google Scholar 

  26. Khovansky, A.G. Newton Polyhedrons and the Euler-Jacobi Formula, Uspehi Math. Nauk, 1978, vol. 33, issue 6.

    Google Scholar 

  27. Bliznyakov, N.M. Computation and Estimation of Index of a Singular Point of Vector Field on a Plane, Deposited in VINITI on June 28, 1979, No. 3041-79.

    Google Scholar 

  28. Bruno, L.D. Local Methods of Nonlinear Analysis of Differential Equations, Nauka, Moscow, 1979.

    Google Scholar 

  29. Zachepa, V.R. and Sapronov, Yu.I. On Local Analysis of Nonlinear Fredholm Equations, Proceedings of the International Conference on Topology, Moscow, 1979.

    Google Scholar 

  30. Zachepa, V.R. On Finitely Defined Solutions to Karman's Equation, Deposited in VINITI on August 14, 1980, No. 3614-80.

    Google Scholar 

  31. Zachepa, V.R. Finitely Defined Equations, Deposited in VINITI on August 14, 1980, No. 3615-80.

    Google Scholar 

  32. Zachepa, V.R. and Sapronov, Yu.I. Regular Branching and Regular Deformations of Nonlinear Fredholm Equations, Deposited in VINITI on August 14, 1980, No. 3617-80.

    Google Scholar 

  33. Chow, S.N., Hale, J.K., and Mallet-Paret, J. Applications of Generic Bifurcation, I-Arch. Rational Mech. Anal, 1975, vol. 59, N 1, II-item., 1976, vol. 62, N 2.

    Google Scholar 

  34. Ize, I.A. Bifurcation Theory for Fredholm Operators, Mem. Amer. Math. Soc., 1976, N 174.

    Google Scholar 

  35. Antman, S.S. Bifurcation Problems for Nonlinearly Elastic Structures, Applications of Bifurcation Theory, New York, 1977.

    Google Scholar 

  36. Knightly, G.H. Some Math. Problems from Plate and Shell Theory, Lecture Notes in Pure and Applied Mathematics, 1977, vol. 19.

    Google Scholar 

  37. Marsden, J.E. Qualitative Methods in Bifurcation Theory, Bull. Amer. Math. Soc., 1978, vol. 84.

    Google Scholar 

  38. Marsden, J.E. On the Geometry of Lyapunov-Schmidt Procedure, Lecture Notes Math., 1979, N 755.

    Google Scholar 

  39. Guimaraes, L.C. Contact Equivalence and Bifurcation Theory, Lecture Notes Math., 1980, N 799.

    Google Scholar 

  40. Hoyle, S.L. Local Solution Manifolds for Nonlinear Equations, Nonlinear Analysis: Theory, Methods, and Applications, 1980, vol. 4, N 2.

    Google Scholar 

  41. Thom, R. Local Topological Properties of Differentiable Mappings, Differential Analysis (Papers presented at the Bombay Colloquium, 1964), 191–202, Oxford University Press, Oxford and New York, 1964.

    Google Scholar 

  42. Mather, J.N. Stability of C∞-Mappings, III: Finitely Determined Mappings, Publ. Math. IHES, 1968, vol. 35.

    Google Scholar 

  43. Chillingworth, D.A. A Global Genericity Theorem for Bifurcation in Variational Problems, J. of Functional Analysis, 1980, vol. 35.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Voronezh State University, 394693, Voronezh, USSR

    Yu. I. Sapronov

Authors
  1. Yu. I. Sapronov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Yurii G. Borisovich Yurii E. Gliklikh A. M. Vershik

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag

About this paper

Cite this paper

Sapronov, Y.I. (1984). Branching of solutions of smooth Fredholm equations. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A.M. (eds) Global Analysis — Studies and Applications I. Lecture Notes in Mathematics, vol 1108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0099551

Download citation

  • DOI: https://doi.org/10.1007/BFb0099551

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13910-2

  • Online ISBN: 978-3-540-39132-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation