On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays
New nonoscillation and oscillation criteria are derived for scalar delay differential equations ̇𝑥(𝑡)+𝑎(𝑡)𝑥(ℎ(𝑡))=0,𝑎(𝑡)≥0,ℎ(𝑡)≤𝑡,𝑡≥𝑡0, and ∑̇𝑥(𝑡)+𝑚𝑘=1𝑎𝑘(𝑡)𝑥(ℎ𝑘(𝑡))=0,𝑎𝑘(𝑡)≥0,ℎ𝑘(𝑡)≤𝑡, and 𝑡≥𝑡0, in the critical case including equations with several unbounded delays, without the usual assumption that...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/417869 |
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| author | Jaromír Baštinec Leonid Berezansky Josef Diblík Zdeněk Šmarda |
| author_facet | Jaromír Baštinec Leonid Berezansky Josef Diblík Zdeněk Šmarda |
| author_sort | Jaromír Baštinec |
| collection | DOAJ |
| description | New nonoscillation and oscillation criteria are derived for scalar delay differential equations ̇𝑥(𝑡)+𝑎(𝑡)𝑥(ℎ(𝑡))=0,𝑎(𝑡)≥0,ℎ(𝑡)≤𝑡,𝑡≥𝑡0, and ∑̇𝑥(𝑡)+𝑚𝑘=1𝑎𝑘(𝑡)𝑥(ℎ𝑘(𝑡))=0,𝑎𝑘(𝑡)≥0,ℎ𝑘(𝑡)≤𝑡,
and 𝑡≥𝑡0, in the critical case including equations with several unbounded delays,
without the usual assumption that the parameters
𝑎,ℎ,𝑎𝑘, and ℎ𝑘 of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations. |
| format | Article |
| id | doaj-art-ed91009fb10c49ef8fc037795b9e9a57 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ed91009fb10c49ef8fc037795b9e9a572025-02-03T06:42:04ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/417869417869On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several DelaysJaromír Baštinec0Leonid Berezansky1Josef Diblík2Zdeněk Šmarda3Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicDepartment of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, IsraelDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicDepartment of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, 61600 Brno, Czech RepublicNew nonoscillation and oscillation criteria are derived for scalar delay differential equations ̇𝑥(𝑡)+𝑎(𝑡)𝑥(ℎ(𝑡))=0,𝑎(𝑡)≥0,ℎ(𝑡)≤𝑡,𝑡≥𝑡0, and ∑̇𝑥(𝑡)+𝑚𝑘=1𝑎𝑘(𝑡)𝑥(ℎ𝑘(𝑡))=0,𝑎𝑘(𝑡)≥0,ℎ𝑘(𝑡)≤𝑡, and 𝑡≥𝑡0, in the critical case including equations with several unbounded delays, without the usual assumption that the parameters 𝑎,ℎ,𝑎𝑘, and ℎ𝑘 of the equations are continuous functions. These conditions improve and extend some known oscillation results in the critical case for delay differential equations.http://dx.doi.org/10.1155/2010/417869 |
| spellingShingle | Jaromír Baštinec Leonid Berezansky Josef Diblík Zdeněk Šmarda On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays Abstract and Applied Analysis |
| title | On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays |
| title_full | On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays |
| title_fullStr | On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays |
| title_full_unstemmed | On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays |
| title_short | On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays |
| title_sort | on the critical case in oscillation for differential equations with a single delay and with several delays |
| url | http://dx.doi.org/10.1155/2010/417869 |
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