Bounds of Solutions of Integrodifferential Equations
Some new integral inequalities are given, and bounds of solutions of the following integro-differential equation are determined: x'(t)-F(t,x(t),∫0tk(t,s,x(t),x(s))ds)=h(t), x(0)=x0, where h:R+→R, k:R+2×R2→R, F:R+×R2→R are continuous functions, R+=[0,∞).
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/571795 |
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| _version_ | 1832565147995996160 |
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| author | Zdeněk Šmarda |
| author_facet | Zdeněk Šmarda |
| author_sort | Zdeněk Šmarda |
| collection | DOAJ |
| description | Some new integral inequalities are given, and bounds of solutions of the following integro-differential equation are determined: x'(t)-F(t,x(t),∫0tk(t,s,x(t),x(s))ds)=h(t), x(0)=x0, where h:R+→R, k:R+2×R2→R, F:R+×R2→R are continuous functions, R+=[0,∞). |
| format | Article |
| id | doaj-art-24bec361e96340478da99100fc0a9c67 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-24bec361e96340478da99100fc0a9c672025-02-03T01:09:00ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/571795571795Bounds of Solutions of Integrodifferential EquationsZdeněk Šmarda0Department of Mathematics, Faculty of Electrical Engineering and Communication, Technická 8, Brno University of Technology, 61600 Brno, Czech RepublicSome new integral inequalities are given, and bounds of solutions of the following integro-differential equation are determined: x'(t)-F(t,x(t),∫0tk(t,s,x(t),x(s))ds)=h(t), x(0)=x0, where h:R+→R, k:R+2×R2→R, F:R+×R2→R are continuous functions, R+=[0,∞).http://dx.doi.org/10.1155/2011/571795 |
| spellingShingle | Zdeněk Šmarda Bounds of Solutions of Integrodifferential Equations Abstract and Applied Analysis |
| title | Bounds of Solutions of Integrodifferential Equations |
| title_full | Bounds of Solutions of Integrodifferential Equations |
| title_fullStr | Bounds of Solutions of Integrodifferential Equations |
| title_full_unstemmed | Bounds of Solutions of Integrodifferential Equations |
| title_short | Bounds of Solutions of Integrodifferential Equations |
| title_sort | bounds of solutions of integrodifferential equations |
| url | http://dx.doi.org/10.1155/2011/571795 |
| work_keys_str_mv | AT zdeneksmarda boundsofsolutionsofintegrodifferentialequations |