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

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.