## 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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