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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 986343, 12 pages
doi:10.1155/2011/986343
Asymptotic Behavior of Solutions to Half-Linear -Difference Equations
Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 61662 Brno, Czech Republic
Received 11 October 2010; Accepted 18 November 2010
Academic Editor: Elena Braverman
Copyright © 2011 Pavel Řehák. 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 derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear -difference equation , with , with , to behave like -regularly varying or -rapidly varying or -regularly bounded functions (that is, the functions , for which a special limit behavior of as is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.