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Periodic solutions to a difference equation with maximum

Author(s): H. D. Voulov
Journal: Proc. Amer. Math. Soc. 131 (2003), 2155-2160.
MSC (2000): Primary 39A10
Posted: November 13, 2002
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Abstract | References | Similar articles | Additional information

Abstract: An open problem posed by G. Ladas is to investigate the difference equation

$\begin{displaymath}x_n=\max\left\{\frac{A}{x_{n-1}}\,,\frac{B}{x_{n-3}}\,,\frac{C} {x_{n-5}}\right\},\quad n=0,1,\ldots,\end{displaymath}$

where

are any nonnegative real numbers with

. We prove that there exists a positive integer

such that every positive solution of this equation is eventually periodic of period

References:

1.: G. Ladas, Open problems and conjectures, J. Diff. Eqns. and Appl., 4(3)(1998), 312.
2.: D. Clark and J.T. Lewis, A Collatz-type difference equation, Congressus Numeratium, 111(1995), 129-135. MR 98b:11008
3.: G. Ladas, Open problems and conjectures, J. Diff. Eqns. and Appl., 2(1996), 339-341.
4.: A.M. Amleh, J. Hoag, and G. Ladas, A difference equation with eventually periodic solutions, Computers and Mathematics with Applications, 36(1998), 401-404. MR 99j:39002
5.: D. Mishev, W.T. Patula, and H.D. Voulov, On a Reciprocal Difference Equation with Maximum, Computers and Mathematics with Applications, 43(2002), 1021-1026.
6.: H.D. Voulov, On the Periodic Character of Some Difference Equations, J. Diff. Eqns. and Appl., 8(9)(2002), 799-810.


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