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Oscillation of second order delay differential equations. (English) Zbl 1141.34341
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 [{\it J. Manojlovic, Y. Shoukaku, T. Tanigawa}, and {\it 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
Full Text:
##### 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) [8] Agarwal, R.; Grace, S.; Regan, D.: Oscillation theory for difference and functional differential equations. (2000)