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Zbl 1167.34028
Xu, Zhiting
Oscillation theorems related to averaging technique for second order emden-fowler type neutral differential equations.
(English)
[J] Rocky Mt. J. Math. 38, No. 2, 649-667 (2008). ISSN 0035-7596

Summary: Some oscillation theorems are established by the averaging techniques for the second order Emden-Fowler type neutral delay differential equation $$(r(t)x'(t))'+q_1(t)|y(t-\sigma_1)|^{\alpha-1} y(t-\sigma_1)+ q_2(t)|y(t-\sigma_2)|^{\beta-1} y(t-\sigma_2)=0,\quad t\ge t_0,$$ where $x(t)=y(t)+p(t)y(t-\tau)$, $\tau$, $\sigma_1$ and $\sigma_2$ are nonnegative constants, $0<\alpha<1$, $\beta>1$, and $r$, $p$, $q_1,q_2\in C(t_0,\infty),\Bbb R)$. These theorems obtained here extend and improve some known results. In particular, two interesting examples that point out the applications of our results are also included.
MSC 2000:
*34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: oscillation; neutral differential equation; Emden-Fowler type; averaging technique; second order

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