Periodic solutions to a difference equation with maximum

Author:
H. D. Voulov

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2155-2160

MSC (2000):
Primary 39A10

Published electronically:
November 13, 2002

MathSciNet review:
1963762

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Abstract | References | Similar Articles | Additional Information

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

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 .

**1.**G. Ladas, Open problems and conjectures,*J. Diff. Eqns. and Appl.*,**4(3)**(1998), 312.**2.**Dean Clark and James T. Lewis,*A Collatz-type difference equation*, Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, FL, 1995), 1995, pp. 129–135. MR**1369346****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*, Comput. Math. Appl.**36**(1998), no. 10-12, 401–404. Advances in difference equations, II. MR**1666157**, 10.1016/S0898-1221(98)80040-0**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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Additional Information

**H. D. Voulov**

Affiliation:
Department of Mathematics, Southern Illinois University at Carbondale, Carbondale, Illinois 62901-4408

Email:
voulovh@yahoo.com

DOI:
https://doi.org/10.1090/S0002-9939-02-06890-9

Keywords:
Periodic solutions,
nonlinear difference equations

Received by editor(s):
February 20, 2002

Published electronically:
November 13, 2002

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2002
American Mathematical Society