一类非线性常微分方程正解的存在性与渐进性

The Existence and Continuance of the Positive Solution of Non-linear Constant Differential Equation

本文讨论了一类非线性二阶常微分方程 0)()()1())((1=-++xuxpxxum 0],1,0(>mx 正解的存在问题,用非线性算子方法证明了正解的存在性、唯一性。并且,给出了这个正解的一个逼近。推广了文献[1]的某些结论。

In this paper, an initial value problem for a nonlinear ordinary differential equation of second order0)()()1())((1=-++xuxpxxum 0],1,0(>mx is considered. Some nonlinear operator methods are used to prove the existence and uniqueness of positive solutions. Moreover, an asymptotic behavior of positive solutions is given. The results improve and generalize some results in [1].