OSCILLATION AND COMPARISON THEOREMS FOR NEUTRAL DIFFERENCE EQUATIONS
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Abstract
In this paper we study qualitative properties of solutions of the neutral difference equation
$$ \Delta(y_n-py_{n-k})+\sum_{i=1}^m q_n^i y_{n-k_i} =0 $$
$$ y_n=A_n \quad \text{ for } n=-M, \cdots, -1, 0$$
where $p \ge 1$, $M =\max\{k, k_1, \cdots, k_m\}$, and $k$, $k_i$, $i =1, \cdots, m$, are nonnegative integers. Riccati techniques are used.
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References
R. K. Brayron and R. A. Willoughby, "On the numerical integration of a symmetric system of difference differential equations of neutral type," J. Math. Anal. Appl., 18 (1969), 182-189.
L. H. Erbe and B. G. Zhang, "Oscillation of discrete analogues of delay equations," Differential and Integral Equations, 2 (1989), N.3, 300-309.
D. A. Gedrgion, E. A. Grove and G. Ladas, "Oscillation of neutral difference equations," Appl. Anal., 33 (1989), N.3-4, 243-253.
- - , "Oscillation of neutral difference equation with variable coefficients," Differential Equations, Lecture Notes in Pure and Applied Mathematics, Ed. Saber Elaydi, Marcel Dekker, 127 (1991), 165-173.
I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarenden Press, Oxford, 1991.
G. Ladas, "Recent developments in the oscillation of delay difference equations," Differential Equa- tions: Stability and Control (1990), Marcel Dekker, 321-332.
G. Ladas, C. G. Philos and Y. G. Sficas, "Necessary and sufficient conditions for the oscillation of difference equations," Liberta Math., 9 (1989), 121-125.
B. S. Lalli, B. G. Zhang and Li Juan Zhao, "On oscillation and existence of positive solutions of neutral difference equations," J. Math. Anal. Appl., 158 (1991), N.l, 213-233.
B. S. Lalli, B. G. Zhang, "On existence of positive solutions and bounded oscillation for neutral difference equations," J. Math. Anal. Appl., 166 (1992), N.l , 272-287.
Zhicheng Wang and Jianshe Yu, "Oscillation criteria for second order nonlinear difference equations," Funkcial Ekvac, 34 (1991), N.2, 313-319.