Keywords
- Bifurcation Point
- Real Case
- Trivial Solution
- Homotopy Class
- Fredholm Operator
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
Adams R. A.: Sobolev Spaces. Academic Press. New-York (1975).
Amann H: Fixed point equations and nonlinear eigenvalue problems in ordered Banach Spaces. SIAM Review 18, 4, (1976), 620–729.
Antman S. S., Rosenheld G.: Global behavior of buckled states of nonlinearly elastic rods-SIAM Review 20, 3 (1978), 513–566.
Alexander J. C., Yorke J.A.: Global bifurcation of periodic orbits. Amer. J. Math. 100 (1978), 263–292.
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.
Berger M.S.: Non linearity and functional analysis. Academic Press, 1977.
Böhme R.: Die Lösung der Verzweingungsgleichungen für nichtlineare Eigenvertprobleme. Math. Z. 127, (1972), 105–126.
Brezis H.: Operateurs maximaux monotones. Math. Studies No. 5, North Holland, 1973.
Chandrasekhar S.: Hydrodynamic and hydromagnetic stability. Oxford U. Press. 1961.
Chow S.N., Mallet-Paret J., Yorke J.A.: Global Hopf bifurcation from a multiple eigenvalue. Nonlinear Anal. 2 (1978), 753–763.
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.
Ciarlet P. G., Rabier P.: Les équations de von Karman. Lect. Notes in Math. 826, Springer Verlag, 1980.
Cronin J.: Fixed points and topological degree in nonlinear analysis. A.M.S. Providence R.I. 1964.
Dancer E.N.: Bifurcation theory in real Banach space. Proc. London Math. Soc. 3, 23 (1971), 699–734.
Dancer E.N.: Bifurcation theory for analytic operators. Proc. London Math. Soc. 3, 26 (1973), 359–384.
Ekeland I., Temam R.: Analyse convexe et problèmes variationnels. Dunod, Paris, 1974.
Friedman A. Partial differential equations. Holt, Rinehart and Winston. New-York, 1969.
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.
Geba K., Granas A.: Infinite dimensional cohomology theories. J. Math. Pures et Appl. 52, 2 (1973), 145–270.
Golubisky M., Guillemin V.: Stable mappings and their singularities. Graduate Texts in Math. No 14, Springer-Verlag, 1973.
Goldberg S.: Unbounded linear operators. Mc Graw-Hill, New-York, 1966.
Iooss G.: Bifurcation of maps and applications. North Holland Math. Studies No 36. Amsterdam, 1979.
Ize J.: Bifurctional theory for Fredholm operators. Memoirs A.M.S. 7, 174, (1976).
Ize J.: Periodic solutions of nonlinear parabolic equations. Comm. in P.D.E. 4, 12, (1979), 1299–1387.
Ize J.: Le problème de bifurcation de Hopf. Seminaire Brezis-Lions, 1975. A paraitre.
Joseph D D. Stability of fluid motions, I. II. Springer-Verlag 1976.
Krasnosel’skii M.A.: Topological methods in the theory of non-linear integral equations. Macmillan, New-York, 1964.
Krasnosel’skii M.A.: Positive solutions of operator equations. P. Noordhoff, Groningen, 1964.
Krasnosel’skii M.A.: Plane vector fields. Academic Press, 1966.
Lions J.L., Magenes E. Nonhomogeneous boundary value problems and application, I. II. Springer-Verlag, New-York, 1972.
Marsden J.E., Mc Cracken M.: The Hopf bifurcation and its applications. Appl. Math. Sciences n. 19. Springer-Verlag, New-York, 1976.
Nirenberg L.: Topics in nonlinear functional analysis. Lecture Notes, Courant Inst., 1974.
Nirenberg L.: Variational and topological methods in nonlinear problems. B.A.M.S. 4, 3, (1981), 267–302.
Nonlinear problems in the physical sciences and biology. Proc. Battelle Summer Inst. Lect. Notes in Math. 322, Springer-Verlag, 1973.
Bifurcation theory and applications in scientific disciplines. Ann. N.Y. Acad. Sci. 316, 1978.
Peitgen H.O., Walther H. O. Ed.: Functional differential equations and approximation of fixed points. Lect. Notes in Math. 730, Springer-Verlag, 1979.
Pimbley G.H.: Eigenfunction branches of nonlinear operators and their bifurcations. Lect. Notes in Math. 104, Springer-Verlag, 1969.
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.
Rabinowitz P.H.: Free vibrations for a semilinear wave equations. C.P.A.M. 31 (1978), 31–68.
Rabinowitz P.H.: Some aspects of nonlinear eigenvalue problems. Rocky Mountain J. of Math. 3, 2, (1973), 161–202.
Sattinger D.H.: Bifurcation and symmetry breaking in applied mathematics, B.A.M.S. 3, 2, (1980), 779–819.
Sattinger D.H.: Topics in stability and bifurcation theory. Lect. Notes in Math. 309, Springer-Verlag, 1973.
Sather D.: Branching of solutions of nonlinear equations. Rocky mountain J. of Math. 3, 2, (1973), 203–250.
Sijbrand J.: Studies in nonlinear stability and bifurcation theory. Thesis, Utrecht, 1981.
Spanier E.: Algebraic topology. Mc. Graw-Hill, 1966.
Temam R.: On the theory and numerical analysis of the Navier-Stokes equations. North Holland, 1977.
Vainberg M.M.: Variational methods for the study of nonlinear operators. Holden day series in Math. Physics, 1964.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1982 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0066238
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-11951-7
Online ISBN: 978-3-540-39539-3
eBook Packages: Springer Book Archive
