On the distance between adjacent zeros of solutions of first order differential equations with distributed delays
We estimate the distance between adjacent zeros of all solutions of the first order differential equation \[ x'(t)+\int_{h(t)}^{t}x(s)d_sR(t,s)=0. \] This form makes it possible to study equations with both discrete and continuous distributions of the delays. The obtained results are new and im...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2015-02-01
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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=3881 |
| _version_ | 1797830555701608448 |
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| author | Hassan A. El-Morshedy Emad Attia |
| author_facet | Hassan A. El-Morshedy Emad Attia |
| author_sort | Hassan A. El-Morshedy |
| collection | DOAJ |
| description | We estimate the distance between adjacent zeros of all solutions of the first order differential equation
\[
x'(t)+\int_{h(t)}^{t}x(s)d_sR(t,s)=0.
\]
This form makes it possible to study equations with both discrete and continuous distributions of the delays. The obtained results are new and improve several known estimations. Some illustrative examples are given to show the advantages of our results over the known ones. |
| first_indexed | 2024-04-09T13:39:03Z |
| format | Article |
| id | doaj.art-0f7c4031297b49a3a4a8f7870dda6c56 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:39:03Z |
| publishDate | 2015-02-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-0f7c4031297b49a3a4a8f7870dda6c562023-05-09T07:53:05ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752015-02-012016811410.14232/ejqtde.2016.1.83881On the distance between adjacent zeros of solutions of first order differential equations with distributed delaysHassan A. El-Morshedy0Emad Attia1Department of Mathematics, Faculty of Science, Damietta University, New Damietta, EgyptDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta, EgyptWe estimate the distance between adjacent zeros of all solutions of the first order differential equation \[ x'(t)+\int_{h(t)}^{t}x(s)d_sR(t,s)=0. \] This form makes it possible to study equations with both discrete and continuous distributions of the delays. The obtained results are new and improve several known estimations. Some illustrative examples are given to show the advantages of our results over the known ones.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3881distance between zerosdistributed delaysfirst order differential equationoscillation |
| spellingShingle | Hassan A. El-Morshedy Emad Attia On the distance between adjacent zeros of solutions of first order differential equations with distributed delays Electronic Journal of Qualitative Theory of Differential Equations distance between zeros distributed delays first order differential equation oscillation |
| title | On the distance between adjacent zeros of solutions of first order differential equations with distributed delays |
| title_full | On the distance between adjacent zeros of solutions of first order differential equations with distributed delays |
| title_fullStr | On the distance between adjacent zeros of solutions of first order differential equations with distributed delays |
| title_full_unstemmed | On the distance between adjacent zeros of solutions of first order differential equations with distributed delays |
| title_short | On the distance between adjacent zeros of solutions of first order differential equations with distributed delays |
| title_sort | on the distance between adjacent zeros of solutions of first order differential equations with distributed delays |
| topic | distance between zeros distributed delays first order differential equation oscillation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=3881 |
| work_keys_str_mv | AT hassanaelmorshedy onthedistancebetweenadjacentzerosofsolutionsoffirstorderdifferentialequationswithdistributeddelays AT emadattia onthedistancebetweenadjacentzerosofsolutionsoffirstorderdifferentialequationswithdistributeddelays |