Necessary and Sufficient Condition for the Solutions of First-Order Neutral Differential Equations to be Oscillatory or Tend to Zero

被引：5

作者：

Santra, Shyam Sundar ^{[1
,2
]}

机构：

[1] Sambalpur Univ, Dept Math, Sambalpur 768019, India

[2] Univ Exeter, Ctr Syst Dynam & Control, Coll Engn Math & Phys Sci, Harrison Bldg, Exeter EX4 4QF, Devon, England

来源：

KYUNGPOOK MATHEMATICAL JOURNAL | 2019年 / 59卷 / 01期

关键词：

Oscillation; nonoscillation; non-linear; delay; neutral differential equations; Knaster-Tarski fixed point theorem and Banach's fixed point theorem; CRITERIA;

D O I：

10.5666/KMJ.2019.59.1.73

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form (x(t) + p(t)x(T(t)))' + q(t)H(x(sigma(t))) = 0 either oscillates or converges to zero as t -> infinity for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

引用

页码：73 / 82

页数：10

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