一类二阶微分方程解的有界性与渐近性

Boundedness and asymptotic behavior of solutions of second order nonlinear differential equation

利用微分不等式技巧讨论了二阶微分方程 (a(t)x′)′ +f(t,x ,x′) =0的解的有界性与渐近性 ,给出了几个重要定理 ,所得结果包含和推广了前人的一些结果 .其中a(t)为定义于R+ =[0 ,+∞ ) 上的正值函数 ,且∫∞01a(t) dt<∞ ,f(t,x ,y)是定义于R+ ×R×R 上的连续函数 .

The boundedness and asymptotic characteristic of solutions of second order nonlinear differential equation(a(t)x′)′+f(t,x,x′)=0 is considered by using the integral inequality. Some important results obtained generalize and improve some of the previous results. a(t) that is defined on +=[0,+∞)is positive function, and∫ ∞ 0[SX(]1a(t) d t<∞, f(t,x,y) that are defined on R +×R×R are continous function.