Distribution of zeros of solutions to functional equations. (English) Zbl 1090.39007
The paper deals with the oscillatory behaviour of solutions of the functional operator equation (1) \(y(t)=(Ty)(t)+f(t)\), \(t\geq 0\), where \(T:L^\infty\to L^\infty\) is a linear positive operator and \(L^\infty\) is the space of measurable essentially bounded functions acting from \(\mathbb{R}_+\) into itself. The main tool used in the considerations is the method of upper and lower solutions combined with a monotone iterative technique. The results obtained in the paper describe the distribution of the zeros of solutions of the equation (1), among others. The authors consider a few particular cases of the equation (1) such as functional equations, difference equations and delay partial differential equations.
Reviewer: J. Banaś (Rzeszów)
MSC:
| 39A11 | Stability of difference equations (MSC2000) |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
| 35R10 | Partial functional-differential equations |
Keywords:
oscillation; nonoscillation; functional operator equation; linear positive operator; method of upper and lower solutions; monotone iterative technique; distribution of the zeros; functional equations; difference equations; delay partial differential equationsReferences:
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