一类高阶中立型非线性方程的正解分类

The Classifications of Positive Solutions of A Class of Higher-order Nonlinear Neutral Equation

时滞微分方程的非振动解的分类及各类非振动解的存在准则是泛函微分方程振动理论的重要课题。通过对一类高阶中立型非线性微分方程正解的分类研究。可提供在Banach空间中,用Schauder不动点定理建立了该类方程正解的分类的几个充要条件,以及该类方程存在趋于零的正解的一个充分条件。

Research on classifications of nonoscillatory solutions of delay differential equation and existence criteria for each type of nonoscillatory solutions is an important subject of the oscillation theory for functional differential equations.The authors of this paper have studied the classifications of positive solutions of a class of higherorder nonlinear neutral equation.Some sufficient and necessary conditions are obtained by Schauder fixed point theorem in the Banach space.The authors have also given a sufficient condition of existence of the equation's positive solutions which converge to zero.