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The necessary and sufficient conditions of existence of periodic solutions of nonautonomous difference equations. (English) Zbl 1025.39009
The results of the authors’ paper [ibid. 131, 461-467 (2002; reviewed above)] are generalized to the nonautonomous case and applied to a rational difference equation.
Reviewer’s remark: In both papers the difference equation has the order $$k+1$$ and not $$n$$.

MSC:
 39A11 Stability of difference equations (MSC2000)
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References:
 [1] Kocic, V.L; Ladas, G, Global asymptotic behaviour of non-linear difference equation of higher order with applications, (1993), Kluwer Academic Publisher Dordrecht · Zbl 0787.39001 [2] Kocic, V.L; Ladas, G; Rodrigues, I.W, On rational recursive sequences, J. math. anal. appl., 173, 127-157, (1993) · Zbl 0777.39002 [3] Leech, J, The rational cuboid revisited, Am. math. monthly, 84, 518-533, (1977) · Zbl 0373.10011 [4] L.A.V. Carvalho, On a method to investigate bifurcation of periodic solutions with integral periods in retarded differential equations (pre-print), I (Msc - Usp), 1993 [5] Hale, J.K, Theory of fuctional differentiations, Applied mathematical sciences, vol. 3, (1977), Springer Berlin [6] Hale, J.K, Ordinary differentiations, (1969), Wiley New York · Zbl 0186.40901 [7] L.A.V. Carvalho, L.A.C. Laderia, On periodic orbits of autonomous differential, difference equations (preprint), Instituto de Ciencias Matematicas de Sao Carlors, 1993 [8] Nussbaum, R.D, On the range of periods of periodic solutions of x(t)=−αf(x(t−1)), J. math. anal. appl., 58, 280-292, (1977) · Zbl 0359.34066 [9] Nussbaum, R.D, Wrigh’s equation has no solutions of period four, (), 445-452 [10] Nussbaum, R.D, A global bifurcation theorem with applications to functional differential equations, J. funct. anal., 19, 319-339, (1975) · Zbl 0314.47041 [11] Chow, S.-N; Mallet-Paret, J, The fuller index and global Hopf bifurcation, J. differential equations, 29, 66-85, (1978) · Zbl 0369.34020
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