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

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
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