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高阶中立型微分方程正解的存在性
引用本文:申建华,庾建设.高阶中立型微分方程正解的存在性[J].数学学报,1996,39(2):145-155.
作者姓名:申建华  庾建设
作者单位:湖南师范大学数学系,湖南大学应用数学系
摘    要: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.

关 键 词:高阶中立型微分方程,正解的存在性,振动
收稿时间:1993-3-19

Existence of Positive Solutions for Higher Order Neutral Differential Equations
Shen Jianhua.Existence of Positive Solutions for Higher Order Neutral Differential Equations[J].Acta Mathematica Sinica,1996,39(2):145-155.
Authors:Shen Jianhua
Institution:Shen Jianhua(Department of Mathematics, Hu'nan Normal University, Changsha 410081, China)Yu Jianshe(Department of Applied Mathematics, Hu'0nan University, Changsha 410082, China)
Abstract: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].
Keywords:higher order neutral differential equation  existence of positive solution  oscillation
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