American Institute of Mathematical Sciences

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2003, 2003(Special): 147-155. doi: 10.3934/proc.2003.2003.147

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

Daria Bugajewska 1, and  Mirosława Zima 2,

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  April 2003

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.
Keywords: functional partial differential equation, system of differential equations of neutral type., linearly bounded operator, existence of global solutions, spectral radius, differential equations with maxima.
Mathematics Subject Classification: Primary: 47H12, 34K05, 35R1.
Citation: Daria Bugajewska, Mirosława Zima. On the spectral radius of linearly bounded operators and existence results for functional-differential equations. Conference Publications, 2003, 2003 (Special) : 147-155. doi: 10.3934/proc.2003.2003.147
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