Address.
Department of Mathematical Analysis, Faculty of
Science, Palacky University,
Tomkova 40, 779 00 Olomouc, Czech Republic
E-mail. stanek@inf.upol.cz
Abstract.
The linear differential equation $(q):y''=q(t)y$
with the uniformly almost-periodic function $q$ is
considered. Necessary and sufficient conditions which guarantee
that all bounded (on $\mathbb R$) solutions of $(q)$ are uniformly
almost-periodic functions are presented. The conditions are
stated by a phase of $(q)$. Next, a class of equations
of the type $(q)$ whose all non-trivial solutions are bounded and
not uniformly almost-periodic
AMSclassification. 34C27, 34A30.
Keywords. Linear second-order differential equation, Appell equation, Kummer equation, uniformly almost-periodic solution, bounded solution, phase.