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

DOI:
https://doi.org/10.1090/S0002-9947-1992-1066450-8

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1992-1066450-8

Keywords:
Nonlinear,
nonautonomous ordinary differential equations,
almost-periodic solutions,
bounded solutions,
Conley index,
skew-product flows

Article copyright:
© Copyright 1992
American Mathematical Society