一类二阶非线性时滞微分方程的振动性定理

OSCILLATION CRITERION FOR CERTAIN SECOND ORDER NONLINEAR DELAY DIFFERENTIAL EQUATION

研究了一类二阶非线性时滞微分方程 x″(t) +F(t,x(t) ,x(τ(t) ) ,x′(t) ,x′(τ(t) ) ) =0 ,t∈[t0 ,∞ )解的振动性 ,借助于一类特殊的Riccati变换 ,得到了该方程振动的一个简单而又直接的判别准则 .

In this paper, the authors study the oscillatiory behavior of certain class of second order nonlinear delay differential equation x″(t)+F(t,x(t),x(τ(t)),x′(t),x′(τ(t)))=0,t∈[t 0,∞). By using a particular Riccati transformation, the authors obtain an simple and direct oscillation criterion for the above equatin.