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Introduction to bifurcation theory

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Differential Equations

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References

  1. Alexander J.C., Antman S.S.: Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems. Univ. of Maryland Technical report. Oct. 1980.

    Google Scholar 

  2. Adams R. A.: Sobolev Spaces. Academic Press. New-York (1975).

    MATH  Google Scholar 

  3. Amann H: Fixed point equations and nonlinear eigenvalue problems in ordered Banach Spaces. SIAM Review 18, 4, (1976), 620–729.

    Article  MathSciNet  MATH  Google Scholar 

  4. Antman S. S., Rosenheld G.: Global behavior of buckled states of nonlinearly elastic rods-SIAM Review 20, 3 (1978), 513–566.

    Article  MathSciNet  MATH  Google Scholar 

  5. Alexander J. C., Yorke J.A.: Global bifurcation of periodic orbits. Amer. J. Math. 100 (1978), 263–292.

    Article  MathSciNet  MATH  Google Scholar 

  6. Alexander J.C., Yorke J.A.: Calculating bifurcation invariants as elements in the homotopy of the general linear group. J. Pure Appl. Algebra 13, (1978), 1–8.

    Article  MathSciNet  MATH  Google Scholar 

  7. Berger M.S.: Non linearity and functional analysis. Academic Press, 1977.

    Google Scholar 

  8. Böhme R.: Die Lösung der Verzweingungsgleichungen für nichtlineare Eigenvertprobleme. Math. Z. 127, (1972), 105–126.

    Article  MathSciNet  MATH  Google Scholar 

  9. Brezis H.: Operateurs maximaux monotones. Math. Studies No. 5, North Holland, 1973.

    Google Scholar 

  10. Chandrasekhar S.: Hydrodynamic and hydromagnetic stability. Oxford U. Press. 1961.

    Google Scholar 

  11. Chow S.N., Mallet-Paret J., Yorke J.A.: Global Hopf bifurcation from a multiple eigenvalue. Nonlinear Anal. 2 (1978), 753–763.

    Article  MathSciNet  MATH  Google Scholar 

  12. Conley C.C. Isolated invariant sets and the Morse index. C.B.M.S. Regional Conf. Series in Math. No. 38. A.M.S. Providence R.I. 1978.

    Google Scholar 

  13. Ciarlet P. G., Rabier P.: Les équations de von Karman. Lect. Notes in Math. 826, Springer Verlag, 1980.

    Google Scholar 

  14. Cronin J.: Fixed points and topological degree in nonlinear analysis. A.M.S. Providence R.I. 1964.

    Google Scholar 

  15. Dancer E.N.: Bifurcation theory in real Banach space. Proc. London Math. Soc. 3, 23 (1971), 699–734.

    Article  MathSciNet  MATH  Google Scholar 

  16. Dancer E.N.: Bifurcation theory for analytic operators. Proc. London Math. Soc. 3, 26 (1973), 359–384.

    Article  MathSciNet  MATH  Google Scholar 

  17. Ekeland I., Temam R.: Analyse convexe et problèmes variationnels. Dunod, Paris, 1974.

    Google Scholar 

  18. Friedman A. Partial differential equations. Holt, Rinehart and Winston. New-York, 1969.

    MATH  Google Scholar 

  19. Fadell F. R., Rabinowitz P.H.: Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems. Invent. Math 45 (1978), 134–174.

    Article  MathSciNet  MATH  Google Scholar 

  20. Geba K., Granas A.: Infinite dimensional cohomology theories. J. Math. Pures et Appl. 52, 2 (1973), 145–270.

    MathSciNet  MATH  Google Scholar 

  21. Golubisky M., Guillemin V.: Stable mappings and their singularities. Graduate Texts in Math. No 14, Springer-Verlag, 1973.

    Google Scholar 

  22. Goldberg S.: Unbounded linear operators. Mc Graw-Hill, New-York, 1966.

    MATH  Google Scholar 

  23. Iooss G.: Bifurcation of maps and applications. North Holland Math. Studies No 36. Amsterdam, 1979.

    Google Scholar 

  24. Ize J.: Bifurctional theory for Fredholm operators. Memoirs A.M.S. 7, 174, (1976).

    MathSciNet  Google Scholar 

  25. Ize J.: Periodic solutions of nonlinear parabolic equations. Comm. in P.D.E. 4, 12, (1979), 1299–1387.

    Article  MathSciNet  MATH  Google Scholar 

  26. Ize J.: Le problème de bifurcation de Hopf. Seminaire Brezis-Lions, 1975. A paraitre.

    Google Scholar 

  27. Joseph D D. Stability of fluid motions, I. II. Springer-Verlag 1976.

    Google Scholar 

  28. Krasnosel’skii M.A.: Topological methods in the theory of non-linear integral equations. Macmillan, New-York, 1964.

    Google Scholar 

  29. Krasnosel’skii M.A.: Positive solutions of operator equations. P. Noordhoff, Groningen, 1964.

    Google Scholar 

  30. Krasnosel’skii M.A.: Plane vector fields. Academic Press, 1966.

    Google Scholar 

  31. Lions J.L., Magenes E. Nonhomogeneous boundary value problems and application, I. II. Springer-Verlag, New-York, 1972.

    Book  MATH  Google Scholar 

  32. Marsden J.E., Mc Cracken M.: The Hopf bifurcation and its applications. Appl. Math. Sciences n. 19. Springer-Verlag, New-York, 1976.

    Google Scholar 

  33. Nirenberg L.: Topics in nonlinear functional analysis. Lecture Notes, Courant Inst., 1974.

    Google Scholar 

  34. Nirenberg L.: Variational and topological methods in nonlinear problems. B.A.M.S. 4, 3, (1981), 267–302.

    Article  MathSciNet  MATH  Google Scholar 

  35. Nonlinear problems in the physical sciences and biology. Proc. Battelle Summer Inst. Lect. Notes in Math. 322, Springer-Verlag, 1973.

    Google Scholar 

  36. Bifurcation theory and applications in scientific disciplines. Ann. N.Y. Acad. Sci. 316, 1978.

    Google Scholar 

  37. Peitgen H.O., Walther H. O. Ed.: Functional differential equations and approximation of fixed points. Lect. Notes in Math. 730, Springer-Verlag, 1979.

    Google Scholar 

  38. Pimbley G.H.: Eigenfunction branches of nonlinear operators and their bifurcations. Lect. Notes in Math. 104, Springer-Verlag, 1969.

    Google Scholar 

  39. Rabinowitz P.H.: Theorie du degré topologique et applications à des problèmes aux limites non linéaires. Lect. Notes, Analyse Numérique Fonctionnelle, Univ. Paris VI, 1975.

    Google Scholar 

  40. Rabinowitz P.H.: Free vibrations for a semilinear wave equations. C.P.A.M. 31 (1978), 31–68.

    MathSciNet  MATH  Google Scholar 

  41. Rabinowitz P.H.: Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. of Math. 3, 2, (1973), 161–202.

    Article  MathSciNet  MATH  Google Scholar 

  42. Sattinger D.H.: Bifurcation and symmetry breaking in applied mathematics, B.A.M.S. 3, 2, (1980), 779–819.

    Article  MathSciNet  MATH  Google Scholar 

  43. Sattinger D.H.: Topics in stability and bifurcation theory. Lect. Notes in Math. 309, Springer-Verlag, 1973.

    Google Scholar 

  44. Sather D.: Branching of solutions of nonlinear equations. Rocky mountain J. of Math. 3, 2, (1973), 203–250.

    Article  MathSciNet  MATH  Google Scholar 

  45. Sijbrand J.: Studies in nonlinear stability and bifurcation theory. Thesis, Utrecht, 1981.

    Google Scholar 

  46. Spanier E.: Algebraic topology. Mc. Graw-Hill, 1966.

    Google Scholar 

  47. Temam R.: On the theory and numerical analysis of the Navier-Stokes equations. North Holland, 1977.

    Google Scholar 

  48. Vainberg M.M.: Variational methods for the study of nonlinear operators. Holden day series in Math. Physics, 1964.

    Google Scholar 

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Djairo Guedes de Figueiredo Chaim Samuel Hönig

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© 1982 Springer-Verlag

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Ize, J. (1982). Introduction to bifurcation theory. In: Guedes de Figueiredo, D., Hönig, C.S. (eds) Differential Equations. Lecture Notes in Mathematics, vol 957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066238

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  • DOI: https://doi.org/10.1007/BFb0066238

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