On the absence of exact means for some bounded functions

I. N. Blinov


Abstract: It is shown that there exist almost periodic functions $f(t)$ such that the function
$$ \varphi(t)=\frac1{c+\int^t_0f(t)\,dt} $$
is bounded but does not have an exact mean value. This fact implies that there are first-order Bernoulli differential equations with almost periodic coefficients such that some bounded solutions do not have exact mean values.
Bibliography: 2 titles.

UDC: 517.9

MSC: Primary 42A75, 34C28; Secondary 34C27

Received: 21.09.1982

 English version: Mathematics of the USSR-Izvestiya, 1984, 23:3, 431–447

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