二阶微分方程的非振动定理

NONOSCILLATION THEOREMS OF SECOND ORDER DIFFERENTIAL EQUATIONS

本文讨论了齐次线性、非齐次线性及非线性二阶微分方程的非振动问题。给出了齐次线性方程非振动的一个充要条件,同时也推出了非齐次线性及非线性二阶方程非振动的一些充分条件。

In this paper,we consider the nonoscillation of the following equations (p(t)x′)′+q(t)x=0 (1) p(t)x″+r(t)x′+q(t)x=0 (2) (p(t)x′)′+q(t)x=f(t) (3) (p(t)x′)′+q(t)x=f(t,x,x′) (4) We give a necessary and sufficient condition for nonoscilation of equations(1)and(2), and some sufficient conditions for non-oscilation of equations(3)and(4)also be given.