zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Asymptotically periodic solutions of Volterra system of difference equations. (English) Zbl 1202.39013
This paper is mainly concerned with the following system of Volterra difference equations: $$x_s(n+1)=a_s(n)+b_s(n)x_s(n)+\sum_{p=1}^r\sum_{i=0}^n K_{sp}(n,i)x_p(i),\quad s=1,2,\dots,r, \quad n=0,1,2,\dots.$$ By using Schauder’s fixed point theorem, the authors prove that the above Volterra difference system has at least an asymptotically periodic solution. In addition, the author give several examples to illustrate their main results.

39A23Periodic solutions (difference equations)
39A30Stability theory (difference equations)
39A06Linear equations (difference equations)
Full Text: DOI
[1] Agarwal, R. P.: Difference equations and inequalities. Theory, methods, and applications, Monographs and textbooks in pure and applied mathematics (2000)
[2] Elaydi, S. N.: An introduction to difference equations, Undergraduate texts in mathematics (2005)
[3] Kocić, V. L.; Ladas, G.: Global behavior of nonlinear difference equations of higher order with applications, Mathematics and its applications (1993) · Zbl 0779.34057
[4] Elaydi, S. N.; Murakami, S.: Uniform asymptotic stability in linear Volterra difference equations, J. difference equ. Appl. 3, 203-218 (1998) · Zbl 0891.39013 · doi:10.1080/10236199808808097
[5] Morchało, J.; Szmanda, B.: Asymptotic properties of solutions of some Volterra difference equations and second-order difference equations, Nonlinear anal. 63, 801-811 (2005) · Zbl 1224.39022 · doi:10.1016/j.na.2005.02.007
[6] Agarwal, R. P.; Popenda, J.: Periodic solutions of first order linear difference equations, Math. comput. Modelling 22, 11-19 (1995) · Zbl 0871.39002 · doi:10.1016/0895-7177(95)00096-K
[7] Popenda, J.; Schmeidel, E.: On the asymptotically periodic solution of some linear difference equations, Arch. math. 35, No. 1, 13-19 (1999) · Zbl 1051.39010
[8] Popenda, J.; Schmeidel, E.: Asymptotically periodic solution of some linear difference equations, Facta univ. Ser. math. Inform. 14, 31-40 (1999) · Zbl 1017.39004
[9] Furumochi, T.: Periodic solutions of Volterra difference equations and attractivity, Nonlinear anal. 47, 4013-4024 (2001) · Zbl 1042.39500 · doi:10.1016/S0362-546X(01)00520-X
[10] Furumochi, T.: Asymptotically periodic solutions of Volterra difference equations, Vietnam J. Math. 30, 537-550 (2002) · Zbl 1031.39011
[11] Appleby, J.; Györi, I.; Reynolds, D.: On exact convergence rates for solutions of linear systems of Volterra difference equations, J. difference equ. Appl. 12, 1257-1275 (2006) · Zbl 1119.39003 · doi:10.1080/10236190600986594
[12] Diblík, J.; Ružičková, M.; Schmeidel, E.: Asymptotically periodic solutions of Volterra difference equations, Berichte aus der Mathematik 5, 1-12 (2007) · Zbl 1136.39005
[13] Musielak, J.: Wstep do analizy funkcjonalnej, (1976)
[14] Zeidler, E.: Nonlinear functional analysis and its application I, fixed-point theorems, (1986) · Zbl 0583.47050