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An asymptotic theorem for abstract differential equations
Published online by Cambridge University Press: 17 April 2009
Abstract
In this paper, we prove the existence of a continuous one-to-one correspondence between bounded solutions of the equation x′(t) = Ax(t) + b(t) which belong to a certain subclass L+ of and bounded mild solutions of the equation x′(t) = Ax(t) + b(t) + f(t, x(t)) of the form u(t) = ø(t) + Ψ(t), with ø(t) ∈ L+ and .
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 33 , Issue 1 , February 1986 , pp. 139 - 144
- Copyright
- Copyright © Australian Mathematical Society 1986