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On the oscillation and periodic character of a third order rational difference equation
Author(s):
W.
T.
Patula;
H.
D.
Voulov
Journal:
Proc. Amer. Math. Soc.
131
(2003),
905-909.
MSC (2000):
Primary 39A10
Posted:
July 17, 2002
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Abstract:
We prove that every positive solution of the following difference equation:
converges to a period two solution.
References:
- 1.
- R. DeVault, G. Ladas, and S.W. Schultz, On the recursive sequence
 , PAMS 126 (1998), 3257-3261. MR 99a:39009 - 2.
- H. El-Metwally, E.A. Grove, and G. Ladas, A global convergence with applications to periodic solutions, J. Math. Anal. Appl. 245 (2000), 161-170. MR 2001g:39014
- 3.
- H. El-Metwally, E.A. Grove, G. Ladas, and H.D. Voulov, On the global attractivity and the periodic character of some difference equations, J. Diff. Eqn. Appl. 7 (2001), 837-850.
- 4.
- G. Karakostas, Asymptotic 2-periodic difference equations with diagonally self-intervertebral responses, J. Diff. Eqn. Appl. 6(3) (2000), 329-335. MR 2001d:39004
- 5.
- G. Karakostas, Convergence of a difference equation via the full limiting sequences method, Diff. Eqn. and Dyn. Sys. 1 (1993), 289-294. MR 95c:34019
- 6.
- M.R.S. Kulenovic and G. Ladas, Dynamics of Second-Order Rational Difference Equations with Open Problems and Conjectures, Chapman and Hall/CRC, 2002.
- 7.
- G. Ladas, Open problems and conjectures, AMS Joint Math. Meetings, January 2001 (New Orleans), Program #364.
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Additional Information:
W.
T.
Patula
Affiliation:
Department of Mathematics, Southern Illinois University Carbondale, Carbondale, Illinois 62901-4408
Email:
wpatula@math.siu.edu
H.
D.
Voulov
Affiliation:
Department of Mathematics, Southern Illinois University Carbondale, Carbondale, Illinois 62901-4408
Email:
voulovh@yahoo.com
DOI:
10.1090/S0002-9939-02-06611-X
PII:
S 0002-9939(02)06611-X
Keywords:
Periodic solution,
semicycles,
oscillation
Received by editor(s):
May 28, 2001
Received by editor(s) in revised form:
October 22, 2001
Posted:
July 17, 2002
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
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