Abstract
We are going to study equilibrium solutions of evolution equations of the form
where t ≥ 0 is the time and µ is a parameter which lies on the real line − ∞ < µ < ∞.
We assume here that F depends on the present value of U(t) and not on its history. For more general possibilities see Notes for I.
This is a preview of subscription content, log in via an 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
Arnold, V. I. Complements on the Theory of Ordinary Differential Equations. Moscow: Nauka, 1978 (in Russian).
Amann, H., Bazley, N., Kirchgâssner, K. Applications of Nonlinear Analysis in the Physical Science. Boston-London Melbourne: Pitman, 1981.
Gurel O., and Rossler, O., eds. Bifurcation theory and its applications in scientific disciplines. Annals of the New York Academy of Sciences , 316, 1979.
Haken, H., ed. Synergetics. Berlin-Heidelberg-New York: Springer-Verlag, 1977.
Iooss, G. Bifurcation of Maps and Applications. Lecture Notes, Mathematical Studies. Amsterdam: North-Holland, 1979.
Joseph, D. D., Stability of Fluid Motions, land II. Springer Tracts in Natural Philosophy. Vol. 27 and 28. Berlin-Heidelberg-New York: Springer-Verlag, 1976.
Keller, J. and Antman, S., eds. Bifurcation Theory and Nonlinear Eigenvalue Problems. New York: W. A. Benjamin, 1969.
Krasnosel’ski, M. A., Topological Methods in the Theory of Nonlinear Integral Equations. New York: Macmillan, 1964.
Marsden, J. and McCracken, M. The Hopf Bifurcation and Its Applications. Lecture notes in Applied Mathematical Sciences, Vol. 18. Berlin-Heidelberg-New York: Springer-Verlag, 1976.
Pimbley, G. H. Eigenfunction Branches of Nonlinear Operators and Their Bifurcations. Lecture Notes in Mathematics No. 104. Berlin-Heidelberg-New York: Springer- Verlag, 1969.
Rabinowitz, P., ed. Applications of Bifurcation Theory. New York: Academic Press, 1977.
Sattinger, D. H. Topics in Stability and Bifurcation Theory. Lecture Notes in Mathematics No. 309. Berlin-Heidelberg-New York: Springer-Verlag, 1972.
Sattinger, D. H. Group Theoretic Methods in Bifurcation Theory. Lecture Notes in Mathematics No. 762. Berlin-Heidelberg-New York, Springer-Verlag 1980.
Stakgold, I. Branching of solutions of nonlinear equations. SIAM Review B, 289 (1971).
Vainberg, M. M., and Trenogin, V. A., The methods of Lyapunov and Schmidt in the theory of nonlinear equations and their further development. Russ. Math. Surveys 17 (2): 1 (1962).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1980 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Iooss, G., Joseph, D.D. (1980). Equilibrium Solutions of Evolution Problems. In: Elementary Stability and Bifurcation Theory. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9336-8_2
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9336-8_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9338-2
Online ISBN: 978-1-4684-9336-8
eBook Packages: Springer Book Archive