Oscillation and Asymptotic Properties of Second Order Half-Linear Differential Equations with Mixed Deviating Arguments

In this paper, we study oscillation and asymptotic properties for half-linear second order differential equations with mixed argument of the form r(t)(y & PRIME;(t))alpha & PRIME;=p(t)y alpha(tau(t)). Such differential equation may possesses two types of nonoscillatory solutions either from the class N0 (positive decreasing solutions) or N2 (positive increasing solutions). We establish new criteria for N0= null and N2= null provided that delayed and advanced parts of deviating argument are large enough. As a consequence of these results, we provide new oscillatory criteria. The presented results essentially improve existing ones even for a linear case of considered equations.