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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A topological method for bounded solutions of nonautonomous ordinary differential equations
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by James R. Ward PDF
Trans. Amer. Math. Soc. 333 (1992), 709-720 Request permission

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.
References
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 333 (1992), 709-720
  • MSC: Primary 34C11; Secondary 58F27
  • DOI: https://doi.org/10.1090/S0002-9947-1992-1066450-8
  • MathSciNet review: 1066450