On the spectral radius of linearly bounded operators and existence results for functional-differential equations

Daria Bugajewska; Mirosława Zima

doi:10.3934/proc.2003.2003.147

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2003, Volume 2003: 147-155. Doi: 10.3934/proc.2003.2003.147 open access

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On the spectral radius of linearly bounded operators and existence results for functional-differential equations

Daria Bugajewska^1, and
Mirosława Zima²

1.
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul.Umultowska 87, 61-614 Poznań
2.
Institute of Mathematics, Rejtana 16A, 35-310 Rzeszów

Received: June 2002

Revised: March 2003

Published: March 2003

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Abstract

In this paper we formulate conditions, different from the global commutativity, under which one can estimate the spectral radius of the composition of linearly bounded operators. We apply this estimation to prove the existence of global solutions for some functional differential equations and systems of such equations. All our results are illustrated by suitable examples.

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Mathematics Subject Classification: Primary: 47H12, 34K05, 35R10.

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