Unbounded solutions of the max-type difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\} $$

• Autorzy: Christopher Kerbert , Michael Radin
• Języki publikacji: EN

Abstrakty

EN

We investigate the boundedness nature of positive solutions of the difference equation $$ x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\},n = 0,1,..., $$ where {A n}n=0∞ and {B n}n=0∞ are periodic sequences of positive real numbers.

Słowa kluczowe

EN

difference equation; unbounded solutions; eventually periodic solution

Kategorie tematyczne

• 39A10: Difference equations, additive

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2008
• Tom: 6
• Numer: 2
• Strony: 307-324

Daty

wydano

2008-06-01

online

2008-04-15

Twórcy

autor

Christopher Kerbert

• School of Mathematical and Sciences

autor

Michael Radin

• School of Mathematical and Sciences

Bibliografia

• [1] Briden W.J., Grove E.A., Kent C.M., Ladas G., Eventually periodic solutions of \( x_{n + 1} = max\left\{ {\frac{1} {{X_n }},\frac{{A_n }} {{X_{n - 1} }}} \right\} \) , Comm. Appl. Nonlinear Anal., 1999, 6, 31–43
• [2] Briden W.J., Grove E.A., Ladas G., McGrath L.C., On the nonautonomous equation \( x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\} \) , New developments in difference equations and applications, Proceedings of the Third International Conference on Difference Equations and Applications (1–5 Sept. 1997 Taipei Taiwan), Gordon and Breach, Amsterdam, 1999, 49–73
• [3] Grove E.A., Kent C.M., Ladas G., Radin M.A., On \( x_{n + 1} = max\left\{ {\frac{1} {{X_n }},\frac{{A_n }} {{X_{n - 1} }}} \right\} \) with a period 3 parameter, Fields Inst. Commun., 2001, 29, 161–180
• [4] Kent C.M., Radin M.A., On the boundedness nature of positive solutions of the difference equation \( x_{n + 1} = max\left\{ {\frac{{A_n }} {{X_n }},\frac{{B_n }} {{X_{n - 2} }}} \right\} \) with periodic parameters, Proceedings of the Third International DCDIS Conference on Engineering Applications and Computational Algorithms (15 May 2003 Guelph Canada), Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 2003, 11–15

Identyfikatory

DOI

10.2478/s11533-008-0018-8