On the asymptotics of nonlinear difference equations. (English) Zbl 1030.39006

Berg, L.

Z. Anal. Anwend. 21, No. 4, 1061-1074 (2002).

The present paper deals with the asymptotic behavior of solutions of nonlinear difference equations. In particular it verifies seven conjectures raised by M. R. S. Kulenović and G. Ladas concerned with rational difference equations in [Dynamics of second order rational difference equations. With open problems and conjectures. Boca Raton, FL: Chapman & Hall/CRC. xi, 218 p. (2002; Zbl 0981.39011)].

Reviewer: Nguyen Van Minh (Harrisonburg)

MSC:

39A11	Stability of difference equations (MSC2000)
39B05	General theory of functional equations and inequalities

Keywords:

asymptotic; asymptotically periodic solution; nonlinear difference equations; rational difference equations

Citations:

Zbl 0981.39011

References:

[1]	Agarwal, R. P., O’Regan, D. and P. J. Y. Wong: Positive Solutions of Differential, Difference and Integral Equations. Dordrecht et al.: Kluwer Acad. Publ. 1999.
[2]	Berg, L.: Asymptotische Darstellungen und Entwicklungen. Berlin: Dt. Verlag Wiss. 1968. · Zbl 0165.36901
[3]	Krause, U. and T. Nesemann: Differenzengleichungen und diskrete dynamische Sys- teme. Stuttgart-Leipzig: Teubner 1999. · Zbl 0918.39001
[4]	Kulenović, M. R. S. and G. Ladas: Dynamics of Second Order Rational Difference Equations. Boca Raton et al.: Chapman & Hall/CRC 2002. · Zbl 0981.39011
[5]	Pachpatte, B. G.: Inequalities for Finite Difference Equations. New York - Basel: Marcel Dekker 2002. · Zbl 0987.39001