Asymptotic behavior of solutions of discrete Volterra equations

• Autorzy: Migda J , Migda M.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2016.36.2.265

• Języki publikacji: EN

Abstrakty

EN

We consider the nonlinear discrete Volterra equations of non-convolution type [formula] We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior, especially asymptotically polynomial and asymptotically periodic solutions. We use o(ns), for a given nonpositive real s, as a measure of approximation. We also give conditions under which all solutions are asymptotically polynomial.

Słowa kluczowe

EN

Volterra difference equation; prescribed asymptotic behaviour; asymptotically polynomial solution; asymptotically periodic solution; bounded solution

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 2
• Strony: 265--278
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Migda J

• Adam Mickiewicz University Faculty of Mathematics and Computer Science Umultowska 87, 61-614 Poznań, Poland

autor

Migda M.

• Poznań University of Technology Institute of Mathematics Piotrowo 3A, 60-965 Poznań, Poland

Bibliografia

• [1] C.T.H. Baker, Y. Song, Periodic solutions of non-linear discrete Volterra equations with finite memory, J. Comput. Appl. Math. 234 (2010) 9, 2683-2698.
• [2] M.R. Crisci, V.B. Kolmanovskii, E. Russo, A. Vecchio, Bounde.dne.ss of discrete Volterra equations, J. Math. Anal. Appl. 211 (1997), 106-130.
• [3] V.B. Demidovic, A certain criterion for the stability of difference equations, Diff. Urav. 5 (1969), 1247-1255 [in Russian].
• [4] J. Diblik, M. Ruzickova, E. Schmeidel, Asymptotically periodic solutions of Volterra difference equations, Tatra Mt. Math. Publ. 43 (2009), 43-61.
• [5] J. Diblik, M. Ruzickova, L.E. Schmeidel, M. Zbaszyniak, Weighted asymptotically periodic solutions of linear Volterra difference equations, Abstr. Appl. Anal. (2011), Art. ID 370982, 14 pp.
• [6] J. Diblik, E. Schmeidel, On the existence of solutions of linear Volterra difference equations asymptotically equivalent to a given sequence, Appl. Math. Comput. 218 (2012) 18, 9310-9320.
• [7] T. Gronek, E. Schmeidel, Existence of bounded solution of Volterra difference equations via Darbo's fixed-point theorem, J. Difference Equ. Appl. 19 (2013) 10, 1645-1653.
• [8] I. Gyori, E. Awwad, On the boundedness of the solutions in nonlinear discrete Volterra difference equations, Adv. Difference Equ. 2 (2012), 1-20.
• [9] I. Gyori, F. Hartung, Asymptotic behavior of nonlinear difference equations, J. Difference Equ. Appl. 18 (2012) 9, 1485-1509.
• [10] I. Gyori, L. Horvath, Asymptotic representation of the solutions of linear Volterra difference equations, Adv. Difference Equ. (2008), ID 932831, 22 pp.
• [11] I. Gyori, D.W. Reynolds, On asymptotically periodic solutions of linear discrete Volterra equations, Fasc. Math. 44 (2010), 53-67.
• [12] V. Kolmanovskii, L. Shaikhet, Some conditions for boundedness of solutions of difference Volterra equations, Appl. Math. Lett. 16 (2003), 857-862.
• [13] R. Medina, Asymptotic behavior of Volterra difference equations, Comput. Math. Appl. 41 (2001) 5-6, 679-687.
• [14] J. Migda, Asymptotic properties of solutions of nonautonomous difference equations, Arch. Math. (Brno) 46 (2010), 1-11.
• [15] J. Migda, Asymptotically polynomial solutions of difference equations, Adv. Difference Equ. 92 (2013), 16 pp.
• [16] J. Migda, Approximative solutions of difference equations, Electron. J. Qual. Theory Differ. Equ. 13 (2014), 1-26.
• [17] J. Migda, Approximative full solutions of difference equations, Int. J. Difference Equ. 9 (2014), 111-121.
• [18] M. Migda, J. Migda, On the asymptotic behavior of solutions of higher order nonlinear-difference equations, Nonlinear Anal. 47 (2001) 7, 4687-4695.
• [19] M. Migda, J. Migda, Bounded solutions of nonlinear discrete Volterra equations, accepted for publication in Math. Slovaca.
• [20] M. Migda, J. Morchało, Asymptotic properties of solutions of difference equations with several delays and Volterra summation equations, Appl. Math. Comput. 220 (2013), 365-373.
• [21] J. Morchało, Volterra summation equations and second order difference equations, Math. Bohem. 135 (2010) 1, 41-56.
• [22] J. Popenda, Asymptotic properties of solutions of difference equations, Proc. Indian Acad. Sci. Math. Sci. 95 (1986) 2, 141-153.
• [23] A. Zafer, Oscillatory and asymptotic behavior of higher order difference equations, Math. Comput. Modelling 21 (1995) 4, 43-50.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.