Methods of bifurcation theory. (English) Zbl 0487.47039

Chow, Shui-Nee; Hale, Jack K.

Grundlehren der Mathematischen Wissenschaften, Bd. 251. New York - Berlin-Heidelberg: Springer-Verlag. XV, 515 p. DM 128.00; $ 59.60 (1982).

MSC:

47J05	Equations involving nonlinear operators (general)
47-02	Research exposition (monographs, survey articles) pertaining to operator theory
34Cxx	Qualitative theory for ordinary differential equations
35Bxx	Qualitative properties of solutions to partial differential equations
47A55	Perturbation theory of linear operators
47Hxx	Nonlinear operators and their properties
58C15	Implicit function theorems; global Newton methods on manifolds
37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Keywords:

qualitative theory of differential equations; bifurcation surface; Euler- Bernoulli problem of the buckling rod; Hopf bifurcation phenomenon; alternative method; Weierstrass and Malgrange preparation theorems; Newton polygon method; transversality; Sard’s theorem; topological degree; index; theory of Ljusternik-Schnirelmann; implicit function theorem; static bifurcation theory; variational theory; boundary value problems; Kármán and Duffing equations; dynamic bifurcation theory; normal forms; perturbation of spectra