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

Pages: 147 - 155, Issue Special, July 2003

 Abstract        Full Text (168.9K)              

Daria Bugajewska - Faculty of Mathematics and Computer Science, Adam Mickiewicz University, ul.Umultowska 87, 61-614 Poznań, Poland (email)
Mirosława Zima - Institute of Mathematics, Rejtana 16A, 35-310 Rzeszów, Poland (email)

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.

Keywords:  differential equations with maxima, existence of global solutions, functional partial differential equation, linearly bounded operator, spectral radius, system of differential equations of neutral type.
Mathematics Subject Classification:  Primary: 47H12, 34K05, 35R10.

Received: June 2002;      Revised: March 2003;      Published: April 2003.