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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A topological method for bounded solutions of nonautonomous ordinary differential equations

Author: James R. Ward
Journal: Trans. Amer. Math. Soc. 333 (1992), 709-720
MSC: Primary 34C11; Secondary 58F27
MathSciNet review: 1066450
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Abstract: The existence of bounded solutions to nonlinear nonautonomous ordinary differential equations is studied. This is done by associating the given equation to nonlinear autonomous ones by means of a family of skew-product flows related by homotopy. The existence of a bounded solution to the original differential equation is then related to the nontriviality of a certain Conley index associated with the autonomous differential equations. The existence of nontrivial bounded solutions is also considered. The differential equations studied are perturbations of homogeneous ones.

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Keywords: Nonlinear, nonautonomous ordinary differential equations, almost-periodic solutions, bounded solutions, Conley index, skew-product flows
Article copyright: © Copyright 1992 American Mathematical Society