On the existence of periodic solutions of ordinary differential equations with high-frequency summands in a Banach space. (English. Russian original) Zbl 1383.34064
Math. Notes 101, No. 2, 310-319 (2017); translation from Mat. Zametki 100, No. 6, 900-910 (2017).
The author reports results on the existence of periodic solutions in linear ODEs in Banach space. The equation considered in this work is of the form
\[
\frac{du}{dt}+A(\omega,t)u=f(\omega,t),
\]
and the results are obtained for \(\omega\) sufficiently large.
Reviewer: Gheorghe Tigan (Timisoara)
MSC:
| 34C25 | Periodic solutions to ordinary differential equations |
| 34G10 | Linear differential equations in abstract spaces |
Keywords:
ordinary differential equation; Banach space; high-frequency coefficient; rapidly oscillating solutionReferences:
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