Abstract
A bifurcation theorem for the solvability of G(x, λ)=0 is proved when the number of parameters is finite and x is an element of a Banach space. The proof depends on imbedding the given problem into a "higher-dimensional" one and relies on the properties of Fredholm operators. Applications to Hopf bifurcation in finite and infinite dimensions as well as to multiple limit-point bifurcations are indicated.
Original language | English |
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Pages (from-to) | 1189-1194 |
Number of pages | 6 |
Journal | SIAM Journal on Applied Mathematics |
Volume | 42 |
Issue number | 6 |
DOIs | |
Publication status | Published - Dec 1982 |