an:00007836
Zbl 0825.34004
Fal'ko, N. S.
Almost periodic Hill equations with bounded solutions
RU
Mat. Issled. 112, 174-179 (1990).
00127223
1990
j
34A30 34C27 34D99
It is shown that in the case, when \(p\in C^2(\mathbb{R},\mathbb{R})\) is almost periodic and for any \(\bar p\in \bar\Sigma_p\) all the solutions of the equation \(\ddot x=\bar p(t)x\) are bounded, there exists for any \(\varepsilon > 0\) such \(p_ \varepsilon \in C(\mathbb{R},\mathbb{R})\) that \(\sup_ t\| p(t)-p_ \varepsilon(t)\| < \varepsilon\); \(p_\varepsilon\) is almost periodic, the condition of inclusion of the Fourier moduli is fulfilled \(M_{p_ \eta}\subset M_p\), and all solutions of the equation \(\ddot x=p_\varepsilon(t)x\) are almost periodic.