讨论了二阶非线性扰动微分方程(a(t)x’(t))’+Q(t,x)=P(t,x,x’)的振动性,通过利用推广的Gronwall不等式理论,改进和推广了由Wintner和Lighton[2]建立的关于微分方程(a(t)x’(t))’+q(t)x(t)=0的所有解振动的一个经典结果,最后的注解给出了充分的说明.
The oscillation for second order perturbed nonlinear differential equation of the form ( a (t) x' (t) )' + Q(t,x) = P(t,x,x') is discussed. By using the generalized Gronwall inequality, improve and extend the classical result which is obtained by Wintner and Lighton for second order linear differential equation of the form ( a (t) x' (t) )' + q (t) x (t) = 0. Finally, the remark is also included to show the versatility of the result.