Exponential dichotomy and bounded solutions of differential equations in the Fréchet space. (English. Russian original) Zbl 1350.34046
Ukr. Math. J. 66, No. 12, 1781-1792 (2015); translation from Ukr. Mat. Zh. 66, No. 12, 1587-1597 (2014).
Summary: We establish necessary and sufficient conditions for the existence of bounded solutions of linear differential equations in the Fréchet space. The solutions are constructed by means of a strong generalized inverse operator.
MSC:
| 34G10 | Linear differential equations in abstract spaces |
| 34D09 | Dichotomy, trichotomy of solutions to ordinary differential equations |
| 34C11 | Growth and boundedness of solutions to ordinary differential equations |
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