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Zbl 1043.34071
Džurina, J.; Stavroulakis, I. P.
Oscillation criteria for second-order delay differential equations. (English)
[J] Appl. Math. Comput. 140, No. 2-3, 445-453 (2003). ISSN 0096-3003

The paper deals with the second-order nonlinear retarded differential equation $$(r(t)\vert u'(t)\vert^{\alpha -1}u'(t))' +p(t)\vert u[\tau(t)]\vert^{\alpha -1}u[\tau(t)]=0,\tag1$$ where $\alpha$ is a positive number; $r\in C^1(t_0,\infty)$, $r(t)>0$, and $R(t)=\int_{t_0}^tr^{-1/\alpha}(s)ds\to\infty$ as $t\to\infty$; $p\in C(t_0,\infty)$, $p(t)>0$; $\tau\in C^1(t_0,\infty)$, $\tau(t)\leq t$, and $\tau(t)\to\infty$ as $t\to\infty$. The authors establish sufficient conditions for all solutions of (1) to be oscillatory in the case $\alpha\geq 1$, and for $0<\alpha <1$.
[Jan Ohriska (Košice)]

MSC 2000:: *34K11 Oscillation theory of functional-differential equations

Keywords: oscillation theory

Cited in: Zbl 1164.34514 Zbl 1164.34508 Zbl 1096.34048

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