The Distribution of Zeros of Solutions of Differential Equations with a Variable Delay

Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 367)

Abstract

This paper is concerned with the distribution of zeros of solutions of the first order linear differential equations with a variable delay of the form
$$\begin{aligned} x'(t)+P(t)x\left( \tau (t)\right) =0 , \quad t\ge {t}_{0},\nonumber \end{aligned}$$
where P, \(\tau \in C([{t}_{0},\;\infty ),[0,\;\infty ))\), \(\tau (t)\le t\), \(\tau (t)\) is nondecreasing, and \(\lim \limits _{t\rightarrow +\infty }\tau (t)=+\infty \). By introducing a class of new series, we are able to derive sharper upper bounds on the distance between zeros of solutions of the above delay differential equations. Some examples and a table are given to support our accomplishment.

Keywords

Distribution of zeros Oscillation Variable delay 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Fundamental CoursesZhongshan PolytechnicZhongshanPeoples Republic of China
  2. 2.Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen UniversityZhuhaiPeoples Republic of China

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