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A conjecture by G. Ladas. (English) Zbl 0902.39003

Summary: A sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained: \(x_{n+1}=A/x^p_n+B/x^q_{n-1}\), \(n=0,1,\dots\), where \(A,B,p,q,x_{-1},x_0\in(0,\infty)\). A conjecture by G. Ladas [J. Difference Equ. Appl. 1, No. 4, 413-419 (1995; Zbl 0853.39002)] is proved.

MSC:

39A10 Additive difference equations

Citations:

Zbl 0853.39002
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References:

[1] Arciero,M., Ladas,G. and Schultz, S. W., Some open problems about the solutions of the delay difference equation x n+1 =A/x n 2 +1/x n-k p , Proceedings of Georgian Academy of Sciences, Mathematics 1: 3(1993),257–262. · Zbl 0819.39007
[2] De Vault, R., Ladas, G. and Schultz, S. W., On the recursive sequence x{n+1}=A/x n p + B/x n-1 q , Proceeding of the Second International Conference on Difference Equation, Aug. 7–11, 1995, Veszpreu, Hungary, Gordon and Breach Science Publishers.
[3] Kocic V. L., and Ladas,G., Global Asymptotic Behavior of Nonlinear Difference Equations of Higher Order with Applications,Kluwer Academic Publishers,Dordrct, 1993. · Zbl 0787.39001
[4] Ladas, G., Open problems and conjectures,Proceedings of the First International Conference on Difference Equations (San Antonio, 1994),Gordon and Breach Science Publishers,Basel, 1995. · Zbl 1057.39505
[5] Ladas, G., Open problems and conjectures, Journal of Difference Equations and Applications, 1 (1995),413–419. · Zbl 0853.39002
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