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Differential equations in Banach spaces

Published online by Cambridge University Press:  17 April 2009

E.S. Noussair
E.S. Noussair
Affiliation:
School of Mathematics, University of New South Wales, Kensington, New South Wales.
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Abstract

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Let H be a fixed Hilbert space and B(H, H) be the Banach space of bounded linear operators from H to H with the uniform operator topology. Oscillation criteria are obtained for the operator differential equation

where the coefficients A, C are linear operators from B(H, H) to B(H, H), for each t ≤ 0. A solution Y: R+ → B(H, H) is said to be oscillatory if there exists a sequence of points ti ∈ R+, so that ti → ∞ as i → ∞, and Y(ti) fails to have a bounded inverse. The main theorem states that a solution Y is oscillatory if an associated scalar differential equation is oscillatory.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 2 , October 1973 , pp. 219 - 226
Copyright
Copyright © Australian Mathematical Society 1973

References

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