Copyright © 2010 Yuzhen Bai and Lihua Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form (p(t)x'(t))'+∑i=1npi(t)x(t-τi)+∑i=1nqi(t)|x(t-τi)|αisgn x(t-τi)=e(t),  t≥0, where p(t), pi(t), qi(t), and e(t) are continuous functions defined on [0,∞), and p(t)>0, p′(t)≥0, and α1>⋯>αm>1>αm+1>⋯>αn>0. No restriction is imposed on the potentials pi(t), qi(t), and e(t) to be nonnegative. These oscillation criteria extend and improve the results given in the recent papers. An interesting example illustrating the sharpness of our results is also provided.