Oscillation of second order delay differential equations. (English) Zbl 1141.34341

Weng, Aizhi; Sun, Jitao

Appl. Math. Comput. 198, No. 2, 930-935 (2008).

Summary: We establish oscillation criteria for the second order functional equations
\[ \left[x(t)+\sum^l_{i=1}c_i(t)x(t-\tau_i)\right]''+\sum^m_{i=1}p_i(t)x(t-\delta_i)-\sum^n_{i=1}q_i(t)x(t-\sigma_i)=0 \]
and
\[ \left[x(t)+\sum^l_{i=1}c_i(t)x(t-\tau_i)\right]''+\sum^m_{i=1}p_i(t)x(t-\delta_i)-\sum^n_{i=1}q_i(t)x(t-\sigma_i)=f(t). \]
They improve the one recently established by [J. Manojlovic, Y. Shoukaku, T. Tanigawa, and N. Yoshida, Appl. Math. Comp. 181, 853–863 (2006; Zbl 1110.34046)].

MSC:

34K11

Oscillation theory of functional-differential equations

Keywords:

oscillation; second order; delay; differential equation

Citations:

Zbl 1110.34046

References:

[1]	Manojlovic, J.; Shoukaku, Y.; Tanigawa, T.; Yoshida, N., Oscillation criteria for second order differential equations with positive and negative coefficients, Appl. Math. Comp., 181, 853-863 (2006) · Zbl 1110.34046
[2]	Shi, W.; Wang, P., Oscillatory criteria of a class of second-order neutral functional differential equations, Applied. Math. Comp., 146, 211-226 (2003) · Zbl 1037.34059
[3]	Wang, P., Oscillation criteria for second-order neutral equations with distributed deviating arguments, J. Comp. Math. Appl., 47, 1935-1946 (2004) · Zbl 1070.34086
[4]	Lee, C.; Yeh, C., An oscillation theorem, Appl. Math. Lett., 20, 238-240 (2007) · Zbl 1114.34327
[5]	Sun, Y., Oscillation of second order functional differential equations with distributed damping, Appl. Math. Comp., 178, 519-526 (2006) · Zbl 1105.34326
[6]	Wang, P.; Wu, Y., Oscillation of certain second-order functional differential equations with damping, J. Comp. Appl. Math., 157, 49-56 (2003) · Zbl 1032.34066
[7]	Erbe, L.; Kong, Q.; Zheng, B., Oscillation Theory for Functional Differential Equations (1995), Dekker: Dekker New York
[8]	Agarwal, R.; Grace, S.; Regan, D., Oscillation Theory for Difference and Functional Differential Equations (2000), Kluwer Academic Publishers: Kluwer Academic Publishers Netherland