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A generalisation of a theorem of O. Perron for semilinear evolution equations

Published online by Cambridge University Press:  03 February 2016

CIPRIAN PREDA
CIPRIAN PREDA*
Affiliation:
West University of Timişoara, Bd. V. Parvan, no. 4, Timişoara 300223, Romania. e-mail: preda@math.cornell.edu
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Abstract

We generalise a well-known result of O. Perron from the 30s that connects the asymptotic behavior of a linear homogeneous differential equation with the response of the inhomogeneous associated equation to a certain class of inhomogeneities (for this reason, Perron's result is also referred to as “input-output method”, “test function method” or “admissibility”).

Our extension is twofold, on the one hand, through the means of a (non)linear evolution family, we deal with the mild solution of a nonautonomous semilinear evolution equation and on the other hand, we collect a very general class of inhomogeneities, eligible for a Perron-type approach in this case.

From a technical point of view, the Perron input-output scenario is achieved here by using the Green operator.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 160 , Issue 3 , May 2016 , pp. 379 - 399
Copyright
Copyright © Cambridge Philosophical Society 2016 

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