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Oscillation criteria for second-order delay differential equations. (English) Zbl 1043.34071
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 $0<\alpha <1$.

34K11Oscillation theory of functional-differential equations
Full Text: DOI
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