Integral Averages and Oscillation Criteria of Second-Order Nonlinear Differential Equations

摘要

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 ≥ t_0 > 0, (*) where a ∈ C~1 ([t_0, ∞)) is a positive function, q ∈ C([t_0, ∞)) has no restriction on its sign, Ψ ∈ C(R), f ∈ C~1(R) are such that f'(x) ≥ 0 and Ψ(x) > 0, xf(x) > 0 for x≠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.