变号系数微分方程的振荡性质

Oscillatory Behavior on the Dcffcrential Equation with Changeable Sign Coefficient

本文引进“弱振荡”的概念,讨论了带变号系数微分方程(1)及(2)的振荡性问题,给出了有关振荡性的一些判别定理.

In this paper, we study the Oscillatory behavior of equations of the forms x '(t) + p(t)f(x(t))g(x '(t)) = 0 and [G(x '(t))]' + p(t)f(x(t)) = 0 , where p(t)∈ C([to,∞),R), f(x)∈ C(R,R) with xf(x)>0 for x≠0 and f(x) has a continuous derivative on R-[0] with f'(x) ≥ 0 for all x≠0, g(u) ∈ C(R,R) with g(u)>0 foru≠0, g(0) -0 and 1/g(u)du<∞, G(y) =∫0ydu/g(u). No sign condition is assumed on p(t). Four weak oscillation criteria and three oscillation criteria arc obtained.