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2011 Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations
Pavel Řehák
Abstr. Appl. Anal. 2011(SI1): 1-12 (2011). DOI: 10.1155/2011/986343


We derive necessary and sufficient conditions for (some or all) positive solutions of the half-linear q-difference equation Dq(Φ(Dqy(t)))+p(t)Φ(y(itqt))=0, t{qk:k0} with q>1, Φ(u)=|u|α-1sgnu with α>1, to behave like q-regularly varying or q-rapidly varying or q-regularly bounded functions (that is, the functions y, for which a special limit behavior of y(itqt)/y(t) as t is prescribed). A thorough discussion on such an asymptotic behavior of solutions is provided. Related Kneser type criteria are presented.


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Pavel Řehák. "Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations." Abstr. Appl. Anal. 2011 (SI1) 1 - 12, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1208.39009
MathSciNet: MR2746015
Digital Object Identifier: 10.1155/2011/986343

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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