A continuation method on locally convex spaces and applications to ordinary differential equations on noncompact intervals. (English) Zbl 0656.47052

Furi, Massimo; Pera, Patrizia

Ann. Pol. Math. 47, 331-346 (1987).

An extension of the Leray-Schauder continuation principle which contains the Schauder-Tychonoff fixed point theorem is proved.
Applications to the differential systems \[ \dot x(t)=f(t,x(t)),\quad \ddot x(t)+\dot x(t)=f(t,x(t)) \] are given.

Reviewer: L.A.Sakhnovich

MSC:

47H10	Fixed-point theorems
47E05	General theory of ordinary differential operators

Keywords:

Leray-Schauder continuation principle; Schauder-Tychonoff fixed point theorem; differential systems