一类二阶微分方程解的有界性与渐近性

Study on boundedness and asymptotic behavior of solutions of nonlinear differential equation of second order

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质 ,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 ,+∞ )上的正值连续函数 ,且∫∞01a(t) dt<∞ ,f(t,x ,y) 是定义于R+

The boundedness and asymptotic behavior of solutions of second order nonlinear differential equation(a(t)x′)′+f(t,x,x′)=0is considered by using the integral inequality. Some impot results obtaind generalize and improve some of the previous results a(t) that drmod on R_+=[0,+∞)is posi twe function,and∫~∞_01a(t)dt<∞,f(t,x,y) that ar defined on R_+×R×R ar continous function.