Periodic solutions for a differential equation in Banach space

Author:
James H. Lightbourne

Journal:
Trans. Amer. Math. Soc. **238** (1978), 285-299

MSC:
Primary 34G05

DOI:
https://doi.org/10.1090/S0002-9947-1978-0481337-X

MathSciNet review:
0481337

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose *X* is a Banach space, is closed and convex, and is continuous. Then if

() |

In the case that , where

*B*satisfies a dissipative condition and

*C*is compact, we obtain a growth estimate on the measure of noncompactness of trajectories for a class of approximate solutions. This estimate is employed to obtain existence of periodic solutions to (IVP).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1978-0481337-X

Keywords:
Banach space,
dissipative,
measure of noncompactness,
periodic solutions

Article copyright:
© Copyright 1978
American Mathematical Society