Existence of asymptotically periodic solutions of scalar Volterra difference equations

Open access


There is used a version of Schauder’s fixed point theorem to prove the existence of asymptotically periodic solutions of a scalar Volterra difference equation. Along with the existence of asymptotically periodic solutions, sufficient conditions for the nonexistence of such solutions are derived. Results are illustrated on examples.

[1] AGARWAL, R. P.: Difference Equations and Inequalities. Theory, Methods, and Applications (2nd ed.), in: Pure Appl. Math., Vol. 228, Marcel Dekker, Inc., New York, 2000.

[2] AGARWAL, R. P.-POPENDA, J.: Periodic solutions of first order linear differenceequations, Math. Comput. Modelling 22 (1995), 11-19.

[3] ELAYDI, S. N.: An Introduction to Difference Equations (3rd ed.), Undergrad. Texts Math., Springer-Verlag, New York, 2005.

[4] ELAYDI, S. N.-MURAKAMI, S.: Uniform asymptotic stability in linear Volterra differenceequations, J. Difference Equ. Appl. 3 (1998), 203-218.

[5] FURUMOCHI, T.: Periodic solutions of Volterra difference equations and attractivity, Nonlinear Anal. 47 (2001), 4013-4024.

[6] FURUMOCHI, T.: Asymptotically periodic solutions of Volterra difference equations, Vietnam J. Math. 30 (2002), 537-550.

[7] KOCI´C, V. L.-LADAS, G.: Global Behavior of Nonlinear Difference Equations of HigherOrder with Applications, in: Math. Appl., Vol. 256., Kluwer Acad. Publ., Dordrecht, 1993.

[8] MUSIELAK, J.: Wstep do Analizy Funkcjonalnej, PWN, Warszawa, 1976. (In Polish)

[9] POPENDA, J.-SCHMEIDEL, E.: On the asymptotically periodic solution of some lineardifference equations, Arch. Math. (Brno) 35 (1999), 13-19.

[10] POPENDA, J.-SCHMEIDEL, E.: Asymptotically periodic solution of some linear differenceequations, Facta Univ. Ser. Math. Inform. 14 (1999), 31-40.

Tatra Mountains Mathematical Publications

The Journal of Slovak Academy of Sciences

Journal Information

CiteScore 2017: 0.37

SCImago Journal Rank (SJR) 2017: 0.363
Source Normalized Impact per Paper (SNIP) 2017: 0.482

Mathematical Citation Quotient (MCQ) 2016: 0.11

Target Group

researchers in the all fields of mathematical research


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 68 68 27
PDF Downloads 23 23 15