Stability in nonlinear neutral differential equations with variable delays using fixed point theory
The purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. In our consideration we allow the coefficient func...
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| Format: | Article |
| Language: | English |
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University of Szeged
2011-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=547 |
| _version_ | 1797830739699433472 |
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| author | Abdelouaheb Ardjouni Ahcene Djoudi |
| author_facet | Abdelouaheb Ardjouni Ahcene Djoudi |
| author_sort | Abdelouaheb Ardjouni |
| collection | DOAJ |
| description | The purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. In our consideration we allow the coefficient functions to change sign and do not require bounded delays. The obtained results improve and generalize those due to Burton, Zhang and Raffoul. We end by giving three examples to illustrate our work. |
| first_indexed | 2024-04-09T13:40:55Z |
| format | Article |
| id | doaj.art-cab07f86989e431c95d521e57fa572e3 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:40:55Z |
| publishDate | 2011-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-cab07f86989e431c95d521e57fa572e32023-05-09T07:53:01ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752011-06-0120114311110.14232/ejqtde.2011.1.43547Stability in nonlinear neutral differential equations with variable delays using fixed point theoryAbdelouaheb Ardjouni0Ahcene Djoudi1University of Annaba, Annaba, AlgeriaUniversity of Annaba, Annaba, AlgeriaThe purpose of this paper is to use a fixed point approach to obtain asymptotic stability results of a nonlinear neutral differential equation with variable delays. An asymptotic stability theorem with a necessary and sufficient condition is proved. In our consideration we allow the coefficient functions to change sign and do not require bounded delays. The obtained results improve and generalize those due to Burton, Zhang and Raffoul. We end by giving three examples to illustrate our work.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=547fixed pointsstabilityneutral differential equationintegral equationvariable delays |
| spellingShingle | Abdelouaheb Ardjouni Ahcene Djoudi Stability in nonlinear neutral differential equations with variable delays using fixed point theory Electronic Journal of Qualitative Theory of Differential Equations fixed points stability neutral differential equation integral equation variable delays |
| title | Stability in nonlinear neutral differential equations with variable delays using fixed point theory |
| title_full | Stability in nonlinear neutral differential equations with variable delays using fixed point theory |
| title_fullStr | Stability in nonlinear neutral differential equations with variable delays using fixed point theory |
| title_full_unstemmed | Stability in nonlinear neutral differential equations with variable delays using fixed point theory |
| title_short | Stability in nonlinear neutral differential equations with variable delays using fixed point theory |
| title_sort | stability in nonlinear neutral differential equations with variable delays using fixed point theory |
| topic | fixed points stability neutral differential equation integral equation variable delays |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=547 |
| work_keys_str_mv | AT abdelouahebardjouni stabilityinnonlinearneutraldifferentialequationswithvariabledelaysusingfixedpointtheory AT ahcenedjoudi stabilityinnonlinearneutraldifferentialequationswithvariabledelaysusingfixedpointtheory |