zbMATH — the first resource for mathematics

On difference equations with powers as solutions and their connection with invariant curves. (English) Zbl 1260.39002
The authors look for a system of nonlinear difference equations that have power functions as solutions. The elements defining the solutions verify a special case of the so-called “equation of invariant curves”. A connection to self-reversed polynomials is also established. For a particular equation of invariant curves, some algebraic solutions are constructed.

39A10 Additive difference equations
Full Text: DOI
[1] Baron, K.; Jarczyk, W., Recent results on functional equations in a single variable, perspectives and open problems, Aequationes math., 61, 1-48, (2001) · Zbl 0972.39011
[2] Berg, L., On the asymptotics of nonlinear difference equations, Z. anal. anwendungen, 21, 4, 1061-1074, (2002) · Zbl 1030.39006
[3] Berg, L., On the asymptotics of difference equation xn−3=xn(1+xn−1xn−2), J. differ. equat. appl., 14, 1, 105-108, (2008)
[4] Berg, L.; Krüppel, M., Eigenfunctions of two-scale difference equations and Appell polynomials, J. anal. appl., 20, 475-488, (2001) · Zbl 0986.39002
[5] L. Berg, S. Stević, On the asymptotics of the difference equation yn(1+yn−1⋯yn−k+1)=yn−k, J. Differ. Equat. Appl. (in press), doi:10.1080/10236190903203820.
[6] Boas, R.P.; Buck, R.C., Polynomial expansions of analytic functions, (1958), Springer Verlag Berlin-Göttingen-Heidelberg · Zbl 0082.05702
[7] Elsayed, E.M., On the difference equation xn+1=xn−5/(±1−xn−2xn−5), Thai. J. math., 7, 1, 1-8, (2009)
[8] Iričanin, B.; Stević, S., On some rational difference equations, Ars combin., 92, 67-72, (2009) · Zbl 1224.39014
[9] Kahlig, P.; Matkowska, A.; Matkowski, J., On a class of a composite functional equation in a single variable, Aequationes math., 52, 260-283, (1996) · Zbl 0861.39013
[10] Kent, C.M., Convergence of solutions in a nonhyperbolic case, Nonlinear anal., 47, 4651-4665, (2001) · Zbl 1042.39507
[11] Kuczma, M., Functional equations in a single variable, (1968), PWN-Polish Scientific Publishers Warszawa · Zbl 0196.16403
[12] Kuczma, M.; Choczewski, B.; Ger, R., Iterative functional equations, Encyclopedia of mathematics and its applications, vol. 32, (1990), Cambridge University Press Cambridge · Zbl 0703.39005
[13] Kulenović, M.R.; Ladas, G., Dynamics of second order rational difference equations, (2002), Chapman & Hall/CRC Boca Raton · Zbl 0981.39011
[14] Stević, S., On the recursive sequence xn+1=xn−1/g(xn), Taiwan. J. math., 6, 3, 405-414, (2002)
[15] Stević, S., More on the difference equation xn+1=xn−1/(1+xn−1xn), Appl. math. E-notes, 4, 80-85, (2004)
[16] Stević, S., Global stability and asymptotics of some classes of rational difference equations, J. math. anal. appl., 316, 60-68, (2006) · Zbl 1090.39009
[17] Stević, S., On positive solutions of a (k+1)th order difference equation, Appl. math. lett., 19, 5, 427-431, (2006) · Zbl 1095.39010
[18] S. Stević, Asymptotics of some classes of higher order difference equations, Discrete Dyn. Nat. Soc. Article ID 56813, (2007), 20p.
[19] Stević, S., Existence of nontrivial solutions of a rational difference equation, Appl. math. lett., 20, 28-31, (2007) · Zbl 1131.39009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.