Bounded solutions of linear differential equations in a banach space
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For a linear inhomogeneous differential equation in a Banach space, we find a criterion for the existence of solutions that are bounded on the entire real axis under the assumption that the homogeneous equation admits an exponential dichotomy on the semiaxes. This result is a generalization of the Palmer lemma to the case of infinite-dimensional spaces. We consider examples of countable systems of ordinary differential equations that have bounded solutions.
KeywordsBanach Space Linear Differential Equation Singular Integral Operator Solvability Condition Bounded Solution
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- 1.Yu. M. Daletskii and M. G. Krein, Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1970).Google Scholar
- 3.I. Ts. Gokhberg and N. Ya. Krupnik, Introduction to the Theory of One-Dimensional Singular Integral Operators [in Russian], Shtiintsa, Kishinev (1973).Google Scholar
- 5.V. S. Korolyuk and A. F. Turbin, Mathematical Foundations of Phase Lumping of Complex Systems [in Russian], Naukova Dumka, Kiev (1978).Google Scholar
- 6.V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow (1980).Google Scholar
- 8.A. M. Samoilenko and Yu. V. Teplinskii, Countable Systems of Differential Equations [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1993).Google Scholar