Necessary and sufficient conditions for oscillation of neutral delay differential equations
In this article, we concerned with oscillation of the neutral delay differential equation $[x(t)-px(t-\tau)]'+qx(t-\sigma)=0$ with constant coefficients. By constructing several suitable auxiliary functions, we obtained some necessary and sufficient conditions for oscillation of all the sol...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-06-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/138/abstr.html |
| _version_ | 1818195705837125632 |
|---|---|
| author | Songbai Guo Wanbiao Ma B. G. Sampath Aruna Pradeep |
| author_facet | Songbai Guo Wanbiao Ma B. G. Sampath Aruna Pradeep |
| author_sort | Songbai Guo |
| collection | DOAJ |
| description | In this article, we concerned with oscillation of the neutral delay
differential equation $[x(t)-px(t-\tau)]'+qx(t-\sigma)=0$ with constant
coefficients. By constructing several suitable auxiliary functions,
we obtained some necessary and sufficient conditions for oscillation
of all the solutions of the aforementioned equation for the cases $0<p<1$
and $p>1$. |
| first_indexed | 2024-12-12T01:22:26Z |
| format | Article |
| id | doaj.art-e151d562a21e45cf8993466d525eb4a4 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T01:22:26Z |
| publishDate | 2014-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-e151d562a21e45cf8993466d525eb4a42022-12-22T00:43:12ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-06-012014138,112Necessary and sufficient conditions for oscillation of neutral delay differential equationsSongbai Guo0Wanbiao Ma1B. G. Sampath Aruna Pradeep2 Univ. of Science and Technology Beijing, China Univ. of Science and Technology Beijing, China Univ. of Science and Technology Beijing, China In this article, we concerned with oscillation of the neutral delay differential equation $[x(t)-px(t-\tau)]'+qx(t-\sigma)=0$ with constant coefficients. By constructing several suitable auxiliary functions, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the aforementioned equation for the cases $0<p<1$ and $p>1$.http://ejde.math.txstate.edu/Volumes/2014/138/abstr.htmlNeutral delay differential equationoscillationcharacteristic equation |
| spellingShingle | Songbai Guo Wanbiao Ma B. G. Sampath Aruna Pradeep Necessary and sufficient conditions for oscillation of neutral delay differential equations Electronic Journal of Differential Equations Neutral delay differential equation oscillation characteristic equation |
| title | Necessary and sufficient conditions for oscillation of neutral delay differential equations |
| title_full | Necessary and sufficient conditions for oscillation of neutral delay differential equations |
| title_fullStr | Necessary and sufficient conditions for oscillation of neutral delay differential equations |
| title_full_unstemmed | Necessary and sufficient conditions for oscillation of neutral delay differential equations |
| title_short | Necessary and sufficient conditions for oscillation of neutral delay differential equations |
| title_sort | necessary and sufficient conditions for oscillation of neutral delay differential equations |
| topic | Neutral delay differential equation oscillation characteristic equation |
| url | http://ejde.math.txstate.edu/Volumes/2014/138/abstr.html |
| work_keys_str_mv | AT songbaiguo necessaryandsufficientconditionsforoscillationofneutraldelaydifferentialequations AT wanbiaoma necessaryandsufficientconditionsforoscillationofneutraldelaydifferentialequations AT bgsampatharunapradeep necessaryandsufficientconditionsforoscillationofneutraldelaydifferentialequations |