Integral averages and oscillation criteria of second-order nonlinear differential equations

The purpose of this paper is to present some new sufficient criteria for the oscillation of all solutions of the second-order nonlinear differential equation (a(t)ψ(x)x′)′+q(t)f(x)=0,t≥t0>0,(*) where α C1 ([t0, ∞)) is a positive function, qC([t0, ∞)) has no restriction on its sign, Ψ C(R), ƒ C1(R) are such that ƒ′() ≥ 0 and Ψ() > 0, xƒ() > 0 for ≠ 0. These criteria are obtained by using a general class of the parameter functions in the averaging techniques and represent extension, as well as improvement of known oscillation criteria of several authors for the generalized Emden-Fowler equation