A local bifurcation theorem is proved under standard transversality assumptions by means of a reduction to finite dimensions. The Krasnosel'skii Bifurcation Theorem is generalized to C 1 - Fredholm maps. Let X and Y be Banach spaces, F: R x X —> Y be C 1 - Fredholm of index 1 and such that F(t, 0) = 0 . If I is a closed, bounded interval at whose endpoints DF(t, 0) is invertible, and the parity of the path is -1 , then I contains a bifurcation point of the equation F(t, x) = 0 . At isolated potential bifurcation points, this sufficient condition for bifurcation is also necessary.
|Titolo:||A local bifurcation theorem for C1-Fredholm maps|
|Data di pubblicazione:||1990|
|Appare nelle tipologie:||1.1 Articolo in rivista|