Electron. J. Diff. Equ., Vol. 2010(2010), No. 167, pp. 1-7.

Comparison theorems for second-order neutral differential equations of mixed type

Tongxing Li

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.

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Tongxing Li
School of Control Science and Engineering, Shandong University
Jinan, Shandong 250061, China
email: litongx2007@163.com

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