On the oscillation of solutions and existence of positive solutions of neutral difference equations. (English) Zbl 0732.39002

Sufficient conditions for the existence of positive solutions and for the oscillation of all solutions of \[ \Delta (x_ n+cx_{n-m})+p_ nx_{n-k}=0,\quad n=0,1,2,..., \] for different values of c with suitable examples are obtained.


39A10 Additive difference equations
39A12 Discrete version of topics in analysis
Full Text: DOI


[1] Brayton, R. K.; Willoughby, R. A., On the numerical integration of a symmetric system of difference-differential equations of neutral type, J. Math. Anal. Appl., 18, 182-189 (1967) · Zbl 0155.47302
[3] Erbe, L. H.; Zhang, B. G., Oscillation of discrete analogues of delay equations, (International Conference on Theory and Applications of Differential Equations. International Conference on Theory and Applications of Differential Equations, Ohio (March 21-25, 1988)) · Zbl 0723.39004
[4] Erbe, L. H.; Zhang, B. G., Oscillation for first order linear differential equations with deviating arguments, Differential and Integral Equations (1988) · Zbl 0723.34055
[6] Hartman, P., Difference equations: Disconjugacy, principal solution, Green’s functions, complete monotonicity, Trans. Amer. Math. Soc., 246, 1-30 (1978) · Zbl 0409.39001
[7] Hooker, J. W.; Patula, W. T., A second-order nonlinear difference equation: oscillation and asymptotic behavior, J. Math. Anal. Appl., 91, 9-29 (1983) · Zbl 0508.39005
[8] Ladas, G.; Sficas, Y. G., Oscillations of neutral delay differential equations, Canad. Math. Bull., 29, 438-445 (1986) · Zbl 0566.34054
[9] Zhang, B. G., Oscillation of first order neutral functional differential equations, J. Math. Anal. Appl., 139, 311-318 (1989) · Zbl 0683.34037
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.