Extensions of Gronwall's inequality with quadratic growth terms and applications
We obtain some new Gronwall type inequalities where, instead of linear growth assumptions, we allow quadratic (or more) growth provided some additional conditions are satisfied. Applications are made to both local and nonlocal boundary value problems for some second order ordinary differential equat...
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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 |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6431 |
| _version_ | 1797830547469238272 |
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| author | Jeff Webb |
| author_facet | Jeff Webb |
| author_sort | Jeff Webb |
| collection | DOAJ |
| description | We obtain some new Gronwall type inequalities where, instead of linear growth assumptions, we allow quadratic (or more) growth provided some additional conditions are satisfied. Applications are made to both local and nonlocal boundary value problems for some second order ordinary differential equations which have quadratic growth in the derivative terms. |
| first_indexed | 2024-04-09T13:37:51Z |
| format | Article |
| id | doaj.art-f62060228e554a77aba3bc266792d8ee |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:51Z |
| publishDate | 2018-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-f62060228e554a77aba3bc266792d8ee2023-05-09T07:53:08ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752018-06-0120186111210.14232/ejqtde.2018.1.616431Extensions of Gronwall's inequality with quadratic growth terms and applicationsJeff Webb0School of Mathematics and Statistics, University of Glasgow, Glasgow, UKWe obtain some new Gronwall type inequalities where, instead of linear growth assumptions, we allow quadratic (or more) growth provided some additional conditions are satisfied. Applications are made to both local and nonlocal boundary value problems for some second order ordinary differential equations which have quadratic growth in the derivative terms.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6431gronwall inequalityquadratic growthsecond order equation |
| spellingShingle | Jeff Webb Extensions of Gronwall's inequality with quadratic growth terms and applications Electronic Journal of Qualitative Theory of Differential Equations gronwall inequality quadratic growth second order equation |
| title | Extensions of Gronwall's inequality with quadratic growth terms and applications |
| title_full | Extensions of Gronwall's inequality with quadratic growth terms and applications |
| title_fullStr | Extensions of Gronwall's inequality with quadratic growth terms and applications |
| title_full_unstemmed | Extensions of Gronwall's inequality with quadratic growth terms and applications |
| title_short | Extensions of Gronwall's inequality with quadratic growth terms and applications |
| title_sort | extensions of gronwall s inequality with quadratic growth terms and applications |
| topic | gronwall inequality quadratic growth second order equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=6431 |
| work_keys_str_mv | AT jeffwebb extensionsofgronwallsinequalitywithquadraticgrowthtermsandapplications |