×

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
PDFBibTeX XMLCite
Full Text: DOI

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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.