二阶非线性扰动微分方程的振动准则

Oscillation criteria for second order perturbed nonlinear differential equation

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W intner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.