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On the Oscillation of Second Order Neutral Differential Equations of Emden-Fowler Type

Authors:	Zhiting Xu

Institution:	(1) South China Normal University, Guangzhou, P.R. China

Abstract:	Some oscillation criteria are established by the averaging technique for the second order neutral delay differential equation of Emden-Fowler type $(a(t)x'(t))'+q_1(t)\| y(t-\sigma_1)\|^{\alpha}\,{\rm sgn}\,y(t-\sigma_1) +q_2(t)\| y(t-\sigma_2)\|^{\beta}\,{\rm sgn}\,y(t-\sigma_2)=0,\quad t \ge t_0,$ where x(t) = y(t) + p(t)y(t − τ), τ, σ₁ and σ₂ are nonnegative constants, α > 0, β > 0, and a, p, q ₁, $q_2\in C(t_0, \infty), {\Bbb R})$ . The results of this paper extend and improve some known results. In particular, two interesting examples that point out the importance of our theorems are also included.

Keywords:	2000 Mathematics Subject Classification: 34C10 34C15
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