Electron. J. Differential Equations, Vol. 2017 (2017), No. 118, pp. 1-14.

Stability of nonlinear neutral delay differential equations with variable delays

Guiling Chen, Dingshi Li, Onno van Gaans, Sjoerd Verduyn Lunel

Abstract:
We present new criteria for asymptotic stability of two classes of nonlinear neutral delay differential equations. By using two auxiliary functions on a contraction condition, we extend the results in [12]. Also we give two examples that illustrate our results.

Submitted December 16, 2016. Published May 3, 2017.
Math Subject Classifications: 34K20, 34K25, 34K40.
Key Words: Asymptotic stability; fixed point theory; variable delay; nonlinear neutral differential equations.

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Guiling Chen
Department of Mathematics
Southwest Jiaotong University
Chengdu 610031, China
email: guiling@home.swjtu.edu.cn
Dingshi Li
Department of Mathematics
Southwest Jiaotong University
Chengdu 610031, China
email: lidingshi2006@163.com
  Onno van Gaans
Mathematical Institute, Leiden University
P.O. Box 9512, 2300 RA
Leiden, The Netherlands
email: vangaans@math.leidenuniv.nl
  Sjoerd Verduyn Lunel
Mathematical Institute, Utrecht University
P.O. Box 80010, 3508 TA
Utrecht, The Netherlands
email: S.M.VerduynLunel@uu.nl

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