Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria
We study non-monotone positive solutions of the second-order linear differential equations: $(p(t)x')' + q(t) x = e(t)$, with positive $p(t)$ and $q(t)$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framewo...
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| Format: | Article |
| Language: | English |
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University of Szeged
2016-10-01
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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=4940 |
| _version_ | 1827951198668324864 |
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| author | Mervan Pašić Satoshi Tanaka |
| author_facet | Mervan Pašić Satoshi Tanaka |
| author_sort | Mervan Pašić |
| collection | DOAJ |
| description | We study non-monotone positive solutions of the second-order linear differential equations: $(p(t)x')' + q(t) x = e(t)$, with positive $p(t)$ and $q(t)$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\theta (t)$ of the corresponding integrable linear equation: $(p(t)\theta')'=e(t)$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions. |
| first_indexed | 2024-04-09T13:38:01Z |
| format | Article |
| id | doaj.art-1dba147eddc145f9980f3b92fc8ffefc |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:01Z |
| publishDate | 2016-10-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-1dba147eddc145f9980f3b92fc8ffefc2023-05-09T07:53:06ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752016-10-0120169312510.14232/ejqtde.2016.1.934940Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteriaMervan Pašić0Satoshi Tanaka1University of Zagreb, Faculty of Electrical Engineering and Computing, Department of Applied Mathematics, Zagreb, CroatiaOkayama University of Science, Okayama, JapanWe study non-monotone positive solutions of the second-order linear differential equations: $(p(t)x')' + q(t) x = e(t)$, with positive $p(t)$ and $q(t)$. For the first time, some criteria as well as the existence and nonexistence of non-monotone positive solutions are proved in the framework of some properties of solutions $\theta (t)$ of the corresponding integrable linear equation: $(p(t)\theta')'=e(t)$. The main results are illustrated by many examples dealing with equations which allow exact non-monotone positive solutions not necessarily periodic. Finally, we pose some open questions.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4940non-monotonic behaviourpositive solutionsexistencenonexistencecriteria |
| spellingShingle | Mervan Pašić Satoshi Tanaka Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria Electronic Journal of Qualitative Theory of Differential Equations non-monotonic behaviour positive solutions existence nonexistence criteria |
| title | Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria |
| title_full | Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria |
| title_fullStr | Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria |
| title_full_unstemmed | Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria |
| title_short | Non-monotone positive solutions of second-order linear differential equations: existence, nonexistence and criteria |
| title_sort | non monotone positive solutions of second order linear differential equations existence nonexistence and criteria |
| topic | non-monotonic behaviour positive solutions existence nonexistence criteria |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=4940 |
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