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Article

Keywords:
Volterra summation equations; oscillation; asymptotic behavior
Summary:
The asymptotic and oscillatory behavior of solutions of Volterra summation equations \[ y_{n}=p_{n} \pm \sum _{s=0}^{n-1}K(n,s)f(s,y_{s}), \ n\in \mathbb{N} \] where $\mathbb{N}=\lbrace 0,1,2,\dots \rbrace $, are studied. Examples are included to illustrate the results.
References:
[1] R. P. Agarwal: Difference Equations and Inequalities. Marcel Dekker, New York, 1992. MR 1155840 | Zbl 0925.39001
[2] R. P. Agarwal, P. J. Y. Wong: Advanced Topics in Diffference Equations. Kluwer Publ., Dordrecht, 1997. MR 1447437
[3] J. R. Graef, E. Thandapani: Oscillatory behavior of solutions of Volterra summation equations. Appl. Math. Lett (to appear). MR 1750064
[4] V. L. Kocic, G. Ladas: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications. Kluwer Publ., Dordrecht, 1993. MR 1247956
[5] S. N. Elaydi: Periodicity and stability of linear Volterra difference systems. (to appear). MR 1260872
[6] S. N. Elaydi, V. L. Kocic: Global stability of a nonlinear Volterra difference systems. Diff. Equations Dynam. Systems 2 (1994), 337–345. MR 1386278
[7] E. Thandapani, B. S. Lalli: Asymptotic behavior and oscillations of a difference equations of Volterra type. Appl. Math. Lett. 7 (1994), 89–93. MR 1349901
[8] V. Lakshmikantham, D. Trigiante: Theory of Difference Equations. Academic Press, New York, 1988. MR 0939611
[9] O. Akinyele: Asymptotic properties of solutions of a Volterra integral equations with delay. An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 30 (1984), 25–30. MR 0800137
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