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Asymptotic property for linear integro-differential systems. (English) Zbl 1161.45006
The authors study the asymptotic property for a certain linear integro-differential system and its perturbation. The variation of constants formula by means of the resolvent matrices and a certain integral inequality with explicit estimate established by the reviewer are used to obtain the results.

MSC:
45M05Asymptotic theory of integral equations
45J05Integro-ordinary differential equations
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References:
[1] Brauer, F.: Asymptotic equivalence and asymptotic behavior of linear systems. Michigan math. J. 9, 33-43 (1962) · Zbl 0111.08603
[2] Cesari, L.: Asymptotic behavior and stability properties in ordinary differential equations. (1963) · Zbl 0111.08701
[3] Choi, S. K.; Koo, N. J.: Asymptotic equivalence between two linear Volterra difference systems. Comput. math. Appl. 47, 461-471 (2004) · Zbl 1053.39007
[4] Choi, S. K.; Koo, N. J.; Dontha, S.: Asymptotic property in variation for nonlinear differential systems. Appl. math. Lett. 18, 117-126 (2005) · Zbl 1075.34042
[5] Choi, S. K.; Koo, N. J.; Goo, Y. H.: Asymptotic property of nonlinear Volterra difference systems. Nonlinear anal. 51, 321-337 (2002) · Zbl 1032.39001
[6] Lakshmikantham, V.; Leela, S.: Differential and integral inequalities with theory and applications. (1969) · Zbl 0177.12403
[7] Lakshmikantham, V.; Rao, M. R. M.: Theory of integro-differential equations. (1995) · Zbl 0849.45004
[8] J. Morchalo, Integral equivalence of two systems of integro-differential equations, in: Proc. Int. Conf. on Differential Equations, Bulgaria, 1985, pp. 841--844
[9] Nohel, J. A.: Asymptotic equivalence of Volterra equations. Ann. mat. Pura appl. 96, 339-347 (1973) · Zbl 0276.45010
[10] Pachpatte, B. G.: On some retarded integral inequalities and applications. J. ineq. Pure appl. Math. 3, No. 2, 1-7 (2002) · Zbl 0994.26017
[11] Rao, M. R. M.; Srinivas, P.: Asymptotic behavior of solutions of Volterra integro-differential equations. Proc. amer. Math. soc. 94, 55-60 (1985) · Zbl 0577.45010
[12] Wintner, A.: Asymptotic equilibria. Amer. J. Math. 68, 125-132 (1946) · Zbl 0063.08289
[13] Zafer, A.: On asymptotic equivalence of linear and quasilinear difference equations. Appl. anal. 84, 899-908 (2005) · Zbl 1087.39018