具变号系数的四阶非线性微分方程的振动性

Oscillation of Four-order Nonlinear Differential Equations with Variable Coefficient

研究了四阶非线性微分方程x(4)(t)+p(t)f(x(t))=0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.所得结论推广了四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 a kind of four-order nonlinear differential equation.x^（4）（t）＋p（t）f（x（t））=0. Two important lemmas and a sufficient condition for the oscillation of all solutions of the equation with variable coefficient p（t） are obtained. We generalize the results of four-order nonlinear differential equation with invariable coefficient.