TY - JOUR AU - Luo, Zhiguo AU - Shen, Jianhua PY - 2001/12/31 Y2 - 2024/03/29 TI - Oscillation criteria for differential equations with piecewise constant argument JF - Tamkang Journal of Mathematics JA - Tamkang J. Math. VL - 32 IS - 4 SE - Papers DO - 10.5556/j.tkjm.32.2001.344 UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/344 SP - 293-304 AB - <p class="MsoNormal" style="margin: 0cm 0cm 0pt;"><span style="font-size: 7.5pt; color: black; font-family: Verdana;" lang="EN-US">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].</span><span style="font-size: 7.5pt;" lang="EN-US"></span></p> ER -