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Abstrakty
We study the existence of an almost periodic solution of discrete Volterra systems by means of fixed point theory. Using discrete variant of exponential dichotomy, we provide sufficient conditions for the existence of an almost periodic solution. Hence, we provide an alternative solution for the open problem proposed in the literature.
Wydawca
Czasopismo
Rocznik
Tom
Strony
320--329
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
- Izmir Katip Celebi University, Department of Engineering Sciences, 35620, Cigli, Izmir, Turkey
autor
- Fayetteville State University, Department of Management, Marketing and Entrepreneurship, 1200 Murchison Road, Fayetteville, NC 28301, USA
Bibliografia
- [1] Burton T. A., Volterra integral and dierential equations, 2nd ed., Mathematics in Science and Engineering, 202, Elsevier B. V., Amsterdam, 2005
- [2] Burton T. A., Furumochi T., Periodic and asymptotically periodic solutions of Volterra integral equations, Funkcial. Ekvac., 1996, 39(1), 87–107
- [3] Clément P., Mitidieri E., Qualitative properties of solutions of Volterra equations in Banach spaces, Israel J. Math., 1988, 64(1), 1–24
- [4] Elaydi S., Periodicity and stability of linear Volterra difference systems, J. Math. Anal. Appl.,1994, 181, 483–492
- [5] Elaydi S., Stability and asymptoticity of Volterra difference equations: A progress report, J. Comput. Appl. Math., 2009, 228(2), 504–513
- [6] Elaydi S., Messina E., Vecchio A., On the asymptotic stability of linear Volterra difference equations of convolution type, J. Dierence Equ. Appl., 2007, 13(12), 1079–1084
- [7] Adivar M., Koyuncuoglu H. C., Raoul Y. N., Periodic and asymptotically periodic solutions of systems of nonlinear difference equations with infinite delay, J. Difference Equ. Appl., 2013, 19(12), 1927–1939
- [8] Adivar M., Koyuncuoglu H. C., Raoul Y. N., Classification of positive solutions of nonlinear systems of Volterra integro-dynamic equations on time scales, Commun. Appl. Anal., 2012, 16(3), 359–375
- [9] Adivar M., Raoul Y. N., Necessary and sufficient conditions for uniform stability of Volterra integro-dynamic equations using new resolvent equation, An. Ştiinţ. Univ. "Ovidius” Constanţa Ser. Mat., 2013, 21(3), 17–32
- [10] Bohr H., Zur theorie der fastperiodischen funktionen I, Acta Math., 1925, 45, 29–127
- [11] Besicovitch A. S., On generalized almost periodic functions, Proc. London Math. Soc., 1926, 25(1), 495–512
- [12] Bochner S., Beitrage zur theorie der fastperiodischen funktionen, Math. Ann., 1926, 96(1), 383–409
- [13] Bochner S., Continuous mappings of almost automorphic and almost periodic functions, Proc. Nat. Acad. Sci. U.S.A., 1964, 52, 907–910
- [14] Stepano W., Ueber einige verallgemeinerungen der fastperiodischen funktionen, Math. Ann., 1925, 45, 473–498
- [15] Besicovitch A. S., Almost periodic functions, Dover Publications, Inc., New York, 1955
- [16] Corduneanu C., Almost periodic functions, Chelsea Publishing Company, New York, 1989
- [17] Bayliss A., Almost periodic solutions to difference equations, Thesis (Ph.D.)–New York University, 1975
- [18] Corduneanu C., Almost periodic discrete processes, Libertas Mathematica, 1982, 2, 159–169
- [19] Diagana T., Almost automorphic type and almost periodic type functions in abstract spaces, Springer, 2013
- [20] Veech W. A., On a theorem of Bochner, Annals of Math., 1967, 86(1), 117–137
- [21] Burton T. A., Furumochi T., Almost periodic solutions of Volterra equations and attractivity, J. Math. Anal. Appl., 1996, 198, 581–599
- [22] Song Y., Almost periodic solutions of discrete Volterra equations, J. Math. Anal. Appl., 2006, 314, 174–194
- [23] Hamaya Y., On the existence of almost periodic solutions of a nonlinear Volterra difference equation, Int. J. Difference Equ., 2007, 2(2), 187–196
- [24] Diagana T., Elaydi S., Yakubu A., Population models in almost periodic environments, J. Differ. Equat. Appl., 2007, 13(4), 239–260
- [25] Lizama C., Mesquita J. G., Almost automorphic solutions of non-autonomous difference equations, J. Math. Anal. Appl., 2013, 407, 339–349
- [26] Adivar M., Koyuncuoglu H. C., Almost automorphic solutions of discrete delayed neutral system, J. Math. Anal. Appl., 2016, 435, 532–550
- [27] Chavez A., Castillo S., Pinto M., Discontinuous almost automorphic functions and almost automorphic solutions of differential equations with piecewise constant arguments, Electron. J. Differ. Equ. Conf., 2014, 2014(56), 1–13
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
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