一类三阶微分方程解的渐近性

The Asymptotic Properties of Solutions to A Class of Third-Order Differential Equations

研究了一类三阶微分方程解的渐近性,方程左端函数中不仅有未知函数,而且含有该未知函数的一阶与二阶导数,利用F.M.Dannan导出的Gronwall-Bellman-Bihari型不等式,并结合微积分技巧和洛必达法则,在一定条件下获得了该类方程解的一种新型的渐近行为.最后给出一个应用实例来证实结果的有效性.

In this paper,we studied the asymptotic behavior of the solution of a class of third-order differential equations.On the left side of the equation,there are not only the unknown function but also its first and second derivatives in the continuous function.We obtained a new kind of asymptotic behavior of the solution of this kind of equation under given fixed conditions by using the Gronwall-Bellman-Bihari inequality derived by F.M.Dannan and combining with calculus techniques and l’Hopital’s rule.Finally,we gave an application example to verify the validity ofthe results.