Oscillation Of Delay And Advanced Differential Equations

In this paper, we will prove some inequalities first. Then some oscillation criteria for equations with delay or advanced argument will be given as simple corollaries of the inequalities. We also proved an analog of famous Hunt and York's Conjecture in advanced case, and finally gave some explicit necessary and sufficient conditions for oscillation for advanced autonomous equations. Especially, we proved that the necessary and sufficient condition for advanced equations with negative coefficients to oscillate is that it's characteristic equation has no real roots.