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Oscillation criteria for second order differential equations with positive and negative coefficients. (English) Zbl 1110.34046

Summary: Some oscillation criteria for the second-order neutral delay differential equations \[ \left[x(t)\pm\sum^l_{i=1}c_i(t)x(t-\tau_i) \right]''+\sum^m_{i=1} p_i(t)x(t-\delta_i)-\sum^n_{i=1}q_i(t)x(t-\sigma_i)=0,\;t>0, \] are established. New oscillation criteria are different from one recently established in the sense that the boundedness of the solution in the results of N. Parhi and S. Chand [J. Indian Math. Soc., New Ser. 66, 227–235 (1999; Zbl 1141.34340)] has been erased., i.e., we give sufficient conditions for the oscillation of all solutions.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations

Citations:

Zbl 1141.34340
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References:

[1] Chuanxi, Q.; Ladas, G., Oscillation in differential equations with positive and negative coefficients, Canad. math. bull., 33, 442-450, (1990) · Zbl 0715.34125
[2] Chuanxi, Q.; Ladas, G., Linearized oscillations for equations with positive and negative coefficients, Hiroshima math. J., 20, 331-340, (1990) · Zbl 0715.34125
[3] Farrel, K.; Grove, E.A.; Ladas, G., Neutral delay differential equations with positive and negative coefficients, Appl. anal., 27, 181-197, (1988) · Zbl 0618.34063
[4] Parhi, N.; Chand, S., Oscillation of second order neutral delay differential equations with positive and negative coefficients, J. ind. math. soc., 66, 227-235, (1999) · Zbl 1141.34340
[5] Ruan, S., Oscillations for first-order neutral differential equations with variable coefficients, Bull. aust. math. soc., 43, 147-152, (1991) · Zbl 0719.34135
[6] Yu, J.S., Neutral differential equations with positive and negative coefficients, Acta math. sin., 34, 517-523, (1991) · Zbl 0738.34040
[7] Yu, J.S.; Wang, Z., Some further results on oscillation of neutral differential equations, Bull. aust. math. soc., 46, 149-157, (1992) · Zbl 0729.34051
[8] Wei, J.J., Sufficient and necessary conditions for the oscillation of first order differential equations with deviating arguments and applications, Acta math. sin., 32, 632-638, (1989) · Zbl 0699.34068
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