一类二阶非线性微分方程解的渐近性态

On the Asymptotic Behavior of the Solutions of a Class of Second-order Nonlinear Differential Equations

在一定条件下，研究了一类二阶非线性微分方程的解的渐近性态，并研究了其解的单调性和可延拓性条件以及其解有界的充分必要条件，得到了这类二阶非线性微分方程的解与二阶线性微分方程的解的渐近关系，以及这两个方程的某些解的等价性条件．

In this paper, we investigate the asympototic behavior of solutions of a class of second order nonlinear differential equation. We discuss the conditions of monotonicity and continuation, and the sufficient and necessary conditions of boundness of the solutions of the equation. And we obtain the asymptotic relationship between the solutions of the equation and those of a class of second order linear differential equation and the equivalent condition of some solutions of the equations.