Oscillation properties for a scalar linear difference equation of mixed type
The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type \Delta x(n)+\sum_{k=-p}^qa_k(n)x(n+k)=0,\quad n>n_0, where $\Delta x(n)=x(n+1)-x(n)$ is the difference operator and $\{a_k(n)\}$ are sequences of real numbers for $k=-p,łdots,q$...
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| Format: | Article |
| Language: | English |
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Institute of Mathematics of the Czech Academy of Science
2016-07-01
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| Series: | Mathematica Bohemica |
| Subjects: | |
| Online Access: | http://mb.math.cas.cz/full/141/2/mb141_2_5.pdf |
| _version_ | 1818560797313335296 |
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| author | Leonid Berezansky Sandra Pinelas |
| author_facet | Leonid Berezansky Sandra Pinelas |
| author_sort | Leonid Berezansky |
| collection | DOAJ |
| description | The aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type
\Delta x(n)+\sum_{k=-p}^qa_k(n)x(n+k)=0,\quad n>n_0,
where $\Delta x(n)=x(n+1)-x(n)$ is the difference operator and $\{a_k(n)\}$ are sequences of real numbers for $k=-p,łdots,q$, and $p>0$, $q\geq0$. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced. |
| first_indexed | 2024-12-14T00:42:52Z |
| format | Article |
| id | doaj.art-0d1ab902e1c342ec89f059f808100862 |
| institution | Directory Open Access Journal |
| issn | 0862-7959 2464-7136 |
| language | English |
| last_indexed | 2024-12-14T00:42:52Z |
| publishDate | 2016-07-01 |
| publisher | Institute of Mathematics of the Czech Academy of Science |
| record_format | Article |
| series | Mathematica Bohemica |
| spelling | doaj.art-0d1ab902e1c342ec89f059f8081008622022-12-21T23:24:16ZengInstitute of Mathematics of the Czech Academy of ScienceMathematica Bohemica0862-79592464-71362016-07-01141216918210.21136/MB.2016.14MB.2016.14Oscillation properties for a scalar linear difference equation of mixed typeLeonid BerezanskySandra PinelasThe aim of this work is to study oscillation properties for a scalar linear difference equation of mixed type \Delta x(n)+\sum_{k=-p}^qa_k(n)x(n+k)=0,\quad n>n_0, where $\Delta x(n)=x(n+1)-x(n)$ is the difference operator and $\{a_k(n)\}$ are sequences of real numbers for $k=-p,łdots,q$, and $p>0$, $q\geq0$. We obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions. Some asymptotic properties are introduced.http://mb.math.cas.cz/full/141/2/mb141_2_5.pdf oscillation difference equation mixed type asymptotic behavior |
| spellingShingle | Leonid Berezansky Sandra Pinelas Oscillation properties for a scalar linear difference equation of mixed type Mathematica Bohemica oscillation difference equation mixed type asymptotic behavior |
| title | Oscillation properties for a scalar linear difference equation of mixed type |
| title_full | Oscillation properties for a scalar linear difference equation of mixed type |
| title_fullStr | Oscillation properties for a scalar linear difference equation of mixed type |
| title_full_unstemmed | Oscillation properties for a scalar linear difference equation of mixed type |
| title_short | Oscillation properties for a scalar linear difference equation of mixed type |
| title_sort | oscillation properties for a scalar linear difference equation of mixed type |
| topic | oscillation difference equation mixed type asymptotic behavior |
| url | http://mb.math.cas.cz/full/141/2/mb141_2_5.pdf |
| work_keys_str_mv | AT leonidberezansky oscillationpropertiesforascalarlineardifferenceequationofmixedtype AT sandrapinelas oscillationpropertiesforascalarlineardifferenceequationofmixedtype |