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Zbl 1188.34086
Han, Zhenlai; Li, Tongxing; Sun, Shurong; Sun, Yibing
Remarks on the paper [Appl. Math. Comput. 207 388-396 (2009)]. (English)
[J] Appl. Math. Comput. 215, No. 11, 3998-4007 (2010). ISSN 0096-3003

Summary: Some sufficient conditions are established for the oscillation of second-order neutral differential equations $$(r(t)\psi (x(t))|Z^\prime (t)|^{\alpha -1}Z^\prime (t))^\prime +q(t)f(x(\sigma(t))) = 0, \quad t\geqslant t_0 >0,$$ where $Z(t) = x(t) +p(t)x(t-\tau )$ and $\alpha >0,0\leqslant p(t)<1 $. On the other hand, some new oscillation criteria are established for the second-order nonlinear neutral delay differential equations $$[r(t)[x(t)+p(t)x(\tau(t))]^\prime ]^\prime +q(t)f(x(\sigma(t))) = 0,\quad t\geqslant t_0>0,$$ where $\int _{t_0}^\infty \frac{\text dt}{r(t)}<\infty , 0\leqslant p(t)\leqslant p_0 < +\infty $. The results obtained here complement and correct some known results by {\it L. Ye} and {\it Z. Xu} [Appl. Math. Comput. 207, No.~2, 388--396 (2009; Zbl 1168.34346)]. Some examples are given to illustrate the main results.

MSC 2000:: *34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: oscillation; neutral delay differential equations; second order

Citations: Zbl 1168.34346

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