zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
On some solvable difference equations and systems of difference equations. (English) Zbl 1253.39001
Summary: We give explicit formulae for solutions of some systems of difference equations, which extend some very particular recent results in the literature and give natural explanations for them, which were omitted in the previous literature.

MSC:
39A05General theory of difference equations
WorldCat.org
Full Text: DOI
References:
[1] A. Andruch-Sobiło and M. Migda, “On the rational recursive sequence xn+1=\alpha xn - 1/(b+cxn - 1),” Tatra Mountains Mathematical Publications, vol. 43, pp. 1-9, 2009. · Zbl 1212.39008
[2] I. Bajo and E. Liz, “Global behaviour of a second-order nonlinear difference equation,” Journal of Difference Equations and Applications, vol. 17, no. 10, pp. 1471-1486, 2011. · Zbl 1232.39014 · doi:10.1080/10236191003639475
[3] L. Berg and S. Stević, “On difference equations with powers as solutions and their connection with invariant curves,” Applied Mathematics and Computation, vol. 217, no. 17, pp. 7191-7196, 2011. · Zbl 1260.39002 · doi:10.1016/j.amc.2011.02.005
[4] L. Berg and S. Stević, “On some systems of difference equations,” Applied Mathematics and Computation, vol. 218, no. 5, pp. 1713-1718, 2011. · Zbl 1243.39009 · doi:10.1016/j.amc.2011.06.050
[5] B. Iri\vcanin and S. Stević, “On some rational difference equations,” Ars Combinatoria, vol. 92, pp. 67-72, 2009. · Zbl 1224.39014
[6] A. S. Kurbanli, “On the behavior of solutions of the system of rational difference equations xn+1=xn - 1/ynxn - 1 - 1),yn+1=yn - 1/(xnyn - 1 - 1) and zn+1=zn - 1/(ynzn - 1 - 1),” Advances in Difference Equations, vol. 2011, 40 pages, 2011. · Zbl 1217.39024 · doi:10.1016/j.mcm.2010.12.009
[7] H. Levy and F. Lessman, Finite Difference Equations, The Macmillan Company, New York, NY, USA, 1961.
[8] G. Papaschinopoulos, C. J. Schinas, and G. Stefanidou, “On the nonautonomous difference equation xn+1=An+(xn - 1p/xnq),” Applied Mathematics and Computation, vol. 217, no. 12, pp. 5573-5580, 2011. · Zbl 1221.39013 · doi:10.1016/j.amc.2010.12.031
[9] G. Papaschinopoulos and G. Stefanidou, “Asymptotic behavior of the solutions of a class of rational difference equations,” International Journal of Difference Equations, vol. 5, no. 2, pp. 233-249, 2010.
[10] S. Stević, “More on a rational recurrence relation,” Applied Mathematics E-Notes, vol. 4, pp. 80-85, 2004. · Zbl 1069.39024 · emis:journals/AMEN/2004/2004.htm · eudml:51567
[11] S. Stević, “A short proof of the Cushing-Henson conjecture,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 37264, 5 pages, 2006. · Zbl 1149.39300 · doi:10.1155/DDNS/2006/37264 · eudml:129355
[12] S. Stević, “On the recursive sequence xn+1=max{c,xnp/xn - 1p},” Applied Mathematics Letters, vol. 21, no. 8, pp. 791-796, 2008. · Zbl 1152.39012 · doi:10.1016/j.aml.2007.08.008
[13] S. Stević, “Global stability of a max-type difference equation,” Applied Mathematics and Computation, vol. 216, no. 1, pp. 354-356, 2010. · Zbl 1193.39009 · doi:10.1016/j.amc.2010.01.020
[14] S. Stević, “On a nonlinear generalized max-type difference equation,” Journal of Mathematical Analysis and Applications, vol. 376, no. 1, pp. 317-328, 2011. · Zbl 1208.39014 · doi:10.1016/j.jmaa.2010.11.041
[15] S. Stević, “On a system of difference equations,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3372-3378, 2011. · Zbl 1242.39017 · doi:10.1016/j.amc.2011.08.079
[16] S. Stević, “On the difference equation xn=xn - 2/(bn+cnxn - 1xn - 2),” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4507-4513, 2011. · Zbl 1220.39011 · doi:10.1080/10236190903203820
[17] S. Stević, “Periodicity of a class of nonautonomous max-type difference equations,” Applied Mathematics and Computation, vol. 217, no. 23, pp. 9562-9566, 2011. · Zbl 1225.39018 · doi:10.1016/j.amc.2011.04.022
[18] S. Stević, “On a system of difference equations with period two coefficients,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4317-4324, 2011. · Zbl 1256.39008 · doi:10.1016/j.amc.2011.10.005
[19] S. Stević, “On a third-order system of difference equations,” Applied Mathematics and Computation, vol. 218, no. 14, pp. 7649-7654, 2012. · Zbl 1243.39011 · doi:10.1016/j.amc.2012.01.034
[20] S. Stević, “On some solvable systems of difference equations,” Applied Mathematics and Computation, vol. 218, no. 9, pp. 5010-5018, 2012. · Zbl 1253.39011 · doi:10.1016/j.amc.2011.10.068
[21] S. Stević, “On the difference equation xn=xn-k/(b+cxn-1 ... xn-k),” Applied Mathematics and Computation, vol. 218, no. 11, pp. 6291-6296, 2012. · Zbl 1246.39010 · doi:10.1016/j.amc.2011.11.107
[22] S. Stević, J. Diblík, B. Iri\vcanin, and Z. \vSmarda, “On a third-order system of difference equations with variable coefficients,” Abstract and Applied Analysis, vol. 2012, Article ID 508523, 22 pages, 2012. · doi:10.1155/2012/508523
[23] S. Stević, J. Diblík, B. Iri\vcanin, and Z. \vSmarda, “On the difference equation xn=anxn - k/(bn+cnxn - 1xn - k),” Abstract and Applied Analysis, vol. 2012, Article ID Article number409237, 20 pages, 2012. · doi:10.1155/2012/409237
[24] S. Stević, J. Diblík, B. Iri\vcanin, and Z. \vSmarda, “On the difference equation xn+1=xnxn - k/(xn - k+1(a+bxnxn - k)),” Abstract and Applied Analysis, vol. 2012, Article ID Article number108047, 9 pages, 2012. · doi:10.1155/2012/108047
[25] N. Touafek and E. M. Elsayed, “On the solutions of systems of rational difference equations,” Mathematical and Computer Modelling, vol. 55, no. 7-8, pp. 1987-1997, 2012. · Zbl 1255.39011 · doi:10.1016/j.mcm.2011.11.058