Permanence in a class of delay differential equations with mixed monotonicity
In this paper we consider a class of delay differential equations of the form $\dot{x}(t)=\alpha (t) h(x(t-\tau), x(t-\sigma))-\beta(t)f(x(t))$, where $h$ is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and u...
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| Format: | Article |
| Language: | English |
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University of Szeged
2018-06-01
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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=6422 |
| _version_ | 1797830549066219520 |
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| author | István Győri Ferenc Hartung Nahed Mohamady |
| author_facet | István Győri Ferenc Hartung Nahed Mohamady |
| author_sort | István Győri |
| collection | DOAJ |
| description | In this paper we consider a class of delay differential equations of the form $\dot{x}(t)=\alpha (t) h(x(t-\tau), x(t-\sigma))-\beta(t)f(x(t))$, where $h$ is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity. |
| first_indexed | 2024-04-09T13:37:52Z |
| format | Article |
| id | doaj.art-f9b5f231a249413b8e6868a83a1ce605 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:52Z |
| publishDate | 2018-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-f9b5f231a249413b8e6868a83a1ce6052023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-06-0120185312110.14232/ejqtde.2018.1.536422Permanence in a class of delay differential equations with mixed monotonicityIstván Győri0Ferenc Hartung1Nahed Mohamady2Department of Mathematics and Computing, University of Pannonia, Veszprém, HungaryDepartment of Mathematics, University of Pannonia, Veszprém, HungaryBenha University, EgyptIn this paper we consider a class of delay differential equations of the form $\dot{x}(t)=\alpha (t) h(x(t-\tau), x(t-\sigma))-\beta(t)f(x(t))$, where $h$ is a mixed monotone function. Sufficient conditions are presented for the permanence of the positive solutions. Our results give also lower and upper estimates of the limit inferior and the limit superior of the solutions via a special solution of an associated nonlinear system of algebraic equations. The results are generated to a more general class of delay differential equations with mixed monotonicity.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6422delay differential equationsmixed monotonicitypersistencepermanence |
| spellingShingle | István Győri Ferenc Hartung Nahed Mohamady Permanence in a class of delay differential equations with mixed monotonicity Electronic Journal of Qualitative Theory of Differential Equations delay differential equations mixed monotonicity persistence permanence |
| title | Permanence in a class of delay differential equations with mixed monotonicity |
| title_full | Permanence in a class of delay differential equations with mixed monotonicity |
| title_fullStr | Permanence in a class of delay differential equations with mixed monotonicity |
| title_full_unstemmed | Permanence in a class of delay differential equations with mixed monotonicity |
| title_short | Permanence in a class of delay differential equations with mixed monotonicity |
| title_sort | permanence in a class of delay differential equations with mixed monotonicity |
| topic | delay differential equations mixed monotonicity persistence permanence |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6422 |
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