We establish necessary and sufficient conditions for the existence of bounded solutions of linear differential equations in the Fréchet space. The solutions are constructed with the use of a strong generalized inverse operator.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 12, pp. 1587–1597, December, 2014.
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Boichuk, A.A., Pokutnyi, A.A. Exponential Dichotomy and Bounded Solutions of Differential Equations in the Fréchet Space. Ukr Math J 66, 1781–1792 (2015). https://doi.org/10.1007/s11253-015-1051-y
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DOI: https://doi.org/10.1007/s11253-015-1051-y