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A necessary and sufficient condition for exponentially bounded existence and uniqueness

Published online by Cambridge University Press:  17 April 2009

David Lowell Lovelady
David Lowell Lovelady
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida, USA.
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Abstract

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A condition which was previously found to be sufficient for global existence and uniqueness of solutions of an ordinary differential equation is shown herein to be necessary, if it is also required that solutions are exponentially bounded.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1973 , pp. 133 - 135
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Coppel, W.A., Stability and asymptotic behavior of differential equations (D.C. Heath, Boston, 1965).Google Scholar
[2]Lovelady, David Lowell and Martin, Robert H. Jr, “A global existence theorem for a nonautonomous differential equation in a Banach space”, Proc. Amer. Math. Soc. 35 (1972), 445–449.CrossRefGoogle Scholar