On asymptotically periodic solutions of linear discrete Volterra equations

• Autorzy: Győri I. , Reynolds D. W.
• Języki publikacji: EN

Abstrakty

EN

We show that a class of linear nonconvolution discrete Volterra equations has asymptotically periodic solutions. We also examine an example for which the calculations can be done explicitly. The results are established using theorems on the boundedness and convergence to a finite limit of solutions of linear discrete Volterra equations.

Słowa kluczowe

EN

asymptotically periodic solutions; Volterra difference equation; asymptotic equilibria

PL

równanie różnicowe

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2010
• Tom: Nr 44
• Strony: 53--67
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Győri I.

autor

Reynolds D. W.

• Department of Mathematics University of Pannonia H-8200 Vezsprém, Egyetem U. 10, Hungary,

Bibliografia

• [1] Appleby J.A.D., Győri I., Reynolds D.W., On exact convergence rates for solutions of linear systems of Volterra difference equations, J. Difference Equ. Appl., 12(12)(2006), 1257–1275.
• [2] Diblík J., Schmeidel E., Ružičková M., Existence of asymptotically periodic solutions of system of Volterra difference equations, J. Difference Equ. Appl., 15(11)(2009), 1165-1177.
• [3] Elaydi S., Periodicity and stability of linear Volterra difference systems, J. Math. Anal. Appl., 181(2)(1994), 483-492.
• [4] Elaydi S., Zhang S., Stability and periodicity of difference equations with finite delay, Funkcial. Ekvac., 37(3)(1994), 401–413.
• [5] Győri I., Horváth L., Asymptotic representation of the solutions of linear Volterra difference equations, Adv. Difference Equ., 22(2008), Art. ID 932831.
• [6] Song Y., Baker C.T.H., Perturbations of Volterra difference equations, J. Difference Equ. Appl., 10(4)(2004), 379-397.
• [7] Song Y., Baker C.T.H., Perturbation theory for discrete Volterra equations, J. Difference Equ. Appl., 9(10)(2003), 969-987.
• [8] Zhang S., The unique existence of periodic solutions of linear Volterra difference equations, J. Math. Anal. Appl., 193(2)(1995), 419–430.