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An existence theorem for ordinary differential equations in Banach spaces

Published online by Cambridge University Press:  17 April 2009

Bogdan Rzepecki
Bogdan Rzepecki
Affiliation:
Institute of Mathematics, A. Mickiewicz University, Matejki 48/49, 60–769 Poznan, Poland.
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Abstract

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We prove the existence of bounded solution of the differential equation y′ = A(t)y + f(t, y) in a Banach space. The method used here is based on the concept of “admissibility” due to Massera and Schäffer when f satisfies the Caratheodory conditions and some regularity condition expressed in terms of the measure of noncompactness α.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 30 , Issue 3 , December 1984 , pp. 449 - 456
Copyright
Copyright © Australian Mathematical Society 1984

References

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