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

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