Oscillation criteria for differential equations with piecewise constant argument

Authors

  • Zhiguo Luo
  • Jianhua Shen

DOI:

https://doi.org/10.5556/j.tkjm.32.2001.344

Abstract

We obtain some new oscillation and nonoscillation criteria for the differential equation with piecewise constant argument $$ x'(t) + a(t)x(t) + b(x) x([t-k]) = 0, $$ where $ a(t) $ and $ b(t) $ are continuous functions on $ [-k, \infty) $, $ b(t) \ge 0 $, $ k $ is a positive integer and $ [ \cdot ] $ denotes the greatest integer function. The method used is based on the treatment of certain difference equation with variable coefficients. Our results extend theorems in [15]. As a special case, our results also improve the conclusions obtained by Aftabizadeh, Wiener and Xu [3].

Author Biography

Zhiguo Luo

Department of Mathematics, Hunan Normal University, Changsha, 410081, P.R. China.

Published

2001-12-31

How to Cite

Luo, Z., & Shen, J. (2001). Oscillation criteria for differential equations with piecewise constant argument. Tamkang Journal of Mathematics, 32(4), 293–304. https://doi.org/10.5556/j.tkjm.32.2001.344

Issue

Section

Papers