Abstract and Applied Analysis
Volume 2011 (2011), Article ID 393875, 8 pages
http://dx.doi.org/10.1155/2011/393875
Research Article

On a Maximal Number of Period Annuli

Yelena Kozmina1 and Felix Sadyrbaev2

1Information Systems and Management Institute, Ludzas Street 91, 1019 Riga, Latvia
2Institute of Mathematics and Computer Science, University of Latvia Rainis Boulevard 29, 1459 Riga, Latvia

Received 30 October 2010; Accepted 30 December 2010

Academic Editor: Elena Braverman

Copyright © 2011 Yelena Kozmina and Felix Sadyrbaev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider equation 𝑥 ″ + 𝑔 ( 𝑥 ) = 0 , where 𝑔 ( 𝑥 ) is a polynomial, allowing the equation to have multiple period annuli. We detect the maximal number of possible period annuli for polynomials of odd degree and show how the respective optimal polynomials can be constructed.