Integrable and continuous solutions of a nonlinear quadratic integral equation
We are concerned here with a nonlinear quadratic integral equation of Volterra type. The existence of at least one $L_1-$ positive solution will be proved under the Carath\`{e}odory condition. Secondly we will make a link between Peano condition and Carath\`{e}odory condition to prove the existence...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Szeged
2008-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=339 |
| _version_ | 1797830793960095744 |
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| author | Ahmed El-Sayed H. H. G. Hashem |
| author_facet | Ahmed El-Sayed H. H. G. Hashem |
| author_sort | Ahmed El-Sayed |
| collection | DOAJ |
| description | We are concerned here with a nonlinear quadratic integral equation of Volterra type. The existence of at least one $L_1-$ positive solution will be proved under the Carath\`{e}odory condition. Secondly we will make a link between Peano condition and Carath\`{e}odory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved. |
| first_indexed | 2024-04-09T13:41:48Z |
| format | Article |
| id | doaj.art-95e68983ff8d4e18927a77d009882c5a |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:41:48Z |
| publishDate | 2008-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-95e68983ff8d4e18927a77d009882c5a2023-05-09T07:52:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752008-08-0120082511010.14232/ejqtde.2008.1.25339Integrable and continuous solutions of a nonlinear quadratic integral equationAhmed El-Sayed0H. H. G. Hashem1Faculty of Science, Alexandria University, Alexandria, EgyptAlexandria University, Alexandria, EgyptWe are concerned here with a nonlinear quadratic integral equation of Volterra type. The existence of at least one $L_1-$ positive solution will be proved under the Carath\`{e}odory condition. Secondly we will make a link between Peano condition and Carath\`{e}odory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=339 |
| spellingShingle | Ahmed El-Sayed H. H. G. Hashem Integrable and continuous solutions of a nonlinear quadratic integral equation Electronic Journal of Qualitative Theory of Differential Equations |
| title | Integrable and continuous solutions of a nonlinear quadratic integral equation |
| title_full | Integrable and continuous solutions of a nonlinear quadratic integral equation |
| title_fullStr | Integrable and continuous solutions of a nonlinear quadratic integral equation |
| title_full_unstemmed | Integrable and continuous solutions of a nonlinear quadratic integral equation |
| title_short | Integrable and continuous solutions of a nonlinear quadratic integral equation |
| title_sort | integrable and continuous solutions of a nonlinear quadratic integral equation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=339 |
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