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Proof of the Favard theorem on the existence of almost-periodic solution for an arbitrary Banach space

V. V. Zhikov

Vladimir Polytechnical Institute

Abstract: The well-known Favard-Amerio theorem on the existence of an almost-periodic solution of a linear equation is based on the geometry of a uniformly convex space, since the almost-periodic solution is found by the minimax condition. In the present note an essentially different method for finding the almost-periodic solution is developed, which enables us to prove the Favard-Amerio theorem for an arbitrary Banach space.

UDC: 519.4

Received: 03.06.1976

 English version: Mathematical Notes, 1978, 23:1, 66–69

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