Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations
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(qt))=0, t∈{qk:k∈N0} with q>1, Φ(u)=|u|α−1sgnu with α>1, to behave like q-regularly varying or...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/986343 |
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| Summary: | 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(qt))=0, t∈{qk:k∈N0} 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(qt)/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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| ISSN: | 1085-3375 1687-0409 |