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On the growth of solutions to second order differential equations in Banach spaces

Published online by Cambridge University Press:  14 November 2011

H. O. Fattorini
H. O. Fattorini
Affiliation:
Departments of Mathematics and System Science, University of California, Los Angeles, California 90024, U.S.A
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Synopsis

We obtain estimates for the exponential growth of the solutions to u″(t) = (A + ζ2I)u(t) in terms of the exponential growth of the solutions to u″(t) = Au(t), where ζ is an arbitrary complex number. Estimates in exponentially weighted L2 norms are also considered in Hilbert space.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 101 , Issue 3-4 , 1985 , pp. 237 - 252
Copyright
Copyright © Royal Society of Edinburgh 1985

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