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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832549431546740736 |
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| author | Pavel Řehák |
| author_facet | Pavel Řehák |
| author_sort | Pavel Řehák |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3990dcc813d14100b0265b30429f80d9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3990dcc813d14100b0265b30429f80d92025-02-03T06:11:20ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/986343986343Asymptotic Behavior of Solutions to Half-Linear q-Difference EquationsPavel Řehák0Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, 61662 Brno, Czech RepublicWe 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.http://dx.doi.org/10.1155/2011/986343 |
| spellingShingle | Pavel Řehák Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations Abstract and Applied Analysis |
| title | Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations |
| title_full | Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations |
| title_fullStr | Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations |
| title_full_unstemmed | Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations |
| title_short | Asymptotic Behavior of Solutions to Half-Linear q-Difference Equations |
| title_sort | asymptotic behavior of solutions to half linear q difference equations |
| url | http://dx.doi.org/10.1155/2011/986343 |
| work_keys_str_mv | AT pavelrehak asymptoticbehaviorofsolutionstohalflinearqdifferenceequations |