高阶中立型微分方程正解的存在性

Existence of Positive Solutions for Higher Order Neutral Differential Equations

考虑ｎ阶中立型微分方程其中ｎ≥１是奇数．在对ｆ较弱的限制条件下，本文获得了方程（＊）当ｐ≠─１时存在正解的充分条件以及当ｐ＝－１时存在有界正解的充分必要条件．本文结果部分地回答了文献［１］中的公开问题．

Consider the n order neutral differential equation where n≥1 is an odd integer. Sufficient conditions are obtained for the existence of a positive solution of Eq. (*) with p≠-1, also, sufficient and necessary conditions are obtained for the existence of a bounded positive solution of Eq. (*) with p =-1. These conditions are weaker for the function f. The results obtained answer partially an open problem in [1].