具变号系数的六阶非线性微分方程的振动性

Oscillation of Sixth-order Nonlinear Differential Equations with Variable Coefficients

研究六阶非线性微分方程的振动性,对振动因子p(t)变号的情况给出了两个重要的引理,并得到方程振动的一个充分性定理.所得结论推广了六阶非线性微分方程当系数不变号时原有的振动性结论.

This paper studies the oscillation of one kind of sixth-order nonlinear differential equation. Two important lemmas and a sufficient condition for the oscillation of all solutions of the equation with variable coefficientare p（t） are obtained. From the result, the sixth-order nonlinear differential equation with invariable coefficient is generalized.