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Estimates of the spectral radius and oscillation behavior of solutions to functional equations. (English) Zbl 1101.39014

Elaydi, Saber (ed.) et al., Proceedings of the 8th international conference on difference equations and applications (ICDEA 2003), Masaryk University, Brno, Czech Republic, July 28–August 1, 2003. Boca Raton, FL: Chapman & Hall/CRC (ISBN 1-58488-536-X/hbk). 97-103 (2005).
The authors discuss sign conditions for solutions of the functional equation \[ y(t)=(Ty)(t)+f(t), \quad t\in[0,\infty), \] where \(T\) is a linear positive operator on the space \(L_{[0,\infty)}^\infty\) of measurable essentially bounded functions. These conditions are in terms of the spectral radius of \(T\) and are based on other (submitted) work of the authors.
For the entire collection see [Zbl 1072.39001].

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
47B38 Linear operators on function spaces (general)
47B65 Positive linear operators and order-bounded operators
47A50 Equations and inequalities involving linear operators, with vector unknowns
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