Choi, Sung Kyu; Goo, Yoon Hoe; Im, Dong Man; Koo, Namjip Total stability in nonlinear discrete Volterra equations with unbounded delay. (English) Zbl 1167.39301 Abstr. Appl. Anal. 2009, Article ID 976369, 13 p. (2009). Summary: We study the total stability in nonlinear discrete Volterra equations with unbounded delay, as a discrete analogue of the results for integrodifferential equations by Y. Hamaya [Funkc. Ekvacioj, Ser. Int. 33, No. 2, 345–362 (1990; Zbl 0709.45012)]. MSC: 39A11 Stability of difference equations (MSC2000) 45G10 Other nonlinear integral equations 39A12 Discrete version of topics in analysis Citations:Zbl 0709.45012 × Cite Format Result Cite Review PDF Full Text: DOI EuDML OA License References: [1] Z. S. Athanassov, “Total stability of sets for nonautonomous differential systems,” Transactions of the American Mathematical Society, vol. 295, no. 2, pp. 649-663, 1986. · Zbl 0587.34040 · doi:10.2307/2000056 [2] Y. Hamaya, “Total stability property in limiting equations of integrodifferential equations,” Funkcialaj Ekvacioj, vol. 33, no. 2, pp. 345-362, 1990. · Zbl 0709.45012 [3] Y. Hino and S. Murakami, “Total stability and uniform asymptotic stability for linear Volterra equations,” Journal of the London Mathematical Society, vol. 43, no. 2, pp. 305-312, 1991. · Zbl 0728.45007 · doi:10.1112/jlms/s2-43.2.305 [4] Y. Hino, “Total stability and uniformly asymptotic stability for linear functional-differential equations with infinite delay,” Funkcialaj Ekvacioj, vol. 24, no. 3, pp. 345-349, 1981. · Zbl 0484.34048 [5] Y. Hino and T. Yoshizawa, “Total stability property in limiting equations for a functional-differential equation with infinite delay,” Akademie V\ued. \vCasopis Pro P Matematiky, vol. 111, no. 1, pp. 62-69, 1986. · Zbl 0599.34071 [6] Y. Hino and S. Murakami, “Total stability in abstract functional differential equations with infinite delay,” in Proceedings of the 6th Colloquium on the Qualitative Theory of Differential Equations (Szeged, 1999), Proc. Colloq. Qual. Theory Differ. Equ., pp. 1-9, Electron. J. Qual. Theory Differ. Equ., Szeged, Hungary, 2000. · Zbl 0973.34063 [7] P. Anderson and S. R. Bernfeld, “Total stability of scalar differential equations determined from their limiting functions,” Journal of Mathematical Analysis and Applications, vol. 257, no. 2, pp. 251-273, 2001. · Zbl 0992.34038 · doi:10.1006/jmaa.2000.6984 [8] T. Yoshizawa, Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, vol. 14 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1975. · Zbl 0304.34051 [9] S. K. Choi and N. Koo, “Almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay,” Advances in Difference Equations, vol. 2008, Article ID 692713, 15 pages, 2008. · Zbl 1167.39302 · doi:10.1155/2008/692713 [10] Y. Hamaya, “Stability property for an integrodifferential equation,” Differential and Integral Equations, vol. 6, no. 6, pp. 1313-1324, 1993. · Zbl 0791.45003 [11] Y. Hamaya, “Periodic solutions of nonlinear integro-differential equations,” The Tohoku Mathematical Journal, vol. 41, no. 1, pp. 105-116, 1989. · Zbl 0689.45017 · doi:10.2748/tmj/1178227869 [12] Y. Song and H. Tian, “Periodic and almost periodic solutions of nonlinear discrete Volterra equations with unbounded delay,” Journal of Computational and Applied Mathematics, vol. 205, no. 2, pp. 859-870, 2007. · Zbl 1122.39007 · doi:10.1016/j.cam.2005.12.042 [13] Y. Song, “Asymptotically almost periodic solutions of nonlinear Volterra difference equations with unbounded delay,” Journal of Difference Equations and Applications, vol. 14, no. 9, pp. 971-986, 2008. · Zbl 1162.39010 · doi:10.1080/10236190801927470 [14] C. Corduneanu, Almost Periodic Functions, Chelsea, New York, NY, USA, 2nd edition, 1989. · Zbl 0672.42008 [15] C. Zhang, Almost Periodic Type Functions and Ergodicity, Science Press, Beijing, China; Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003. · Zbl 1068.34001 [16] J. K. Hale and J. Kato, “Phase space for retarded equations with infinite delay,” Funkcialaj Ekvacioj, vol. 21, no. 1, pp. 11-41, 1978. · Zbl 0383.34055 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.