Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 167, pp. 1-7.
Title: Comparison theorems for second-order neutral
differential equations of mixed type
Author: Tongxing Li (Shandong Univ., Jinan, China)
Abstract:
Three comparison theorems are established for the oscillation
of the second-order neutral differential equations of mixed type
$$
\big(r(t)[x(t)+p_1(t)x(t-\sigma_1)+p_2(t)x(t+\sigma_2)]'\big)'
+q_1(t)x(t-\sigma_3) +q_2(t)x(t+\sigma_4)=0.
$$
Our results are new even when $p_2(t)=q_2(t)=0$. An
example is provided to illustrate the main results.
Submitted October 22, 2010. Published November 24, 2010.
Math Subject Classifications: 34K11.
Key Words: Oscillation; neutral functional differential equations;
mixed type; second-order; comparison theorem.