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Zbl 1025.39016
Shen, Jianhua; Stavroulakis, I.P.
An oscillation criteria for second order functional equations.
(English)
[J] Acta Math. Sci., Ser. B, Engl. Ed. 22, No.1, 56-62 (2002). ISSN 0252-9602

The authors consider the second-order linear functional equation $$x\bigl(g(t)\bigr) =P(t)x(t)+Q(t)x \bigl(g^2(t)\bigr),\ t\ge t_0,$$ where $P,Q,g:[t_0,\infty) \to[0,\infty)$ are given function, $t_0\ge 0$, $g\ne id|_{[t_0,\infty)}$, $\lim_{t\to\infty} g(t)=\infty$. They prove a sufficient condition for the oscillation of all solutions of the equation. This result improves a result of {\it W. Golda} and {\it J. Werbowski} [Funkc. Ekvacioj, Ser. Int. 37, 221-227 (1994; Zbl 0807.39007)].
[Zbigniew Leśniak (Kraków)]
MSC 2000:
*39B22 Functional equations for real functions
39B82 Stability, separation, extension, and related topics

Keywords: second-order linear functional equation; oscillation

Citations: Zbl 0807.39007

Cited in: Zbl 1194.39015

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