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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Hindawi Limited
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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Article |
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doaj-24bec361e96340478da99100fc0a9c672020-11-25T00:24:42ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zdeněk Šmarda |
| spellingShingle |
Zdeněk Šmarda Bounds of Solutions of Integrodifferential Equations Abstract and Applied Analysis |
| author_facet |
Zdeněk Šmarda |
| author_sort |
Zdeněk Šmarda |
| title |
Bounds of Solutions of Integrodifferential Equations |
| title_short |
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_sort |
bounds of solutions of integrodifferential equations |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2011-01-01 |
| 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,∞). |
| url |
http://dx.doi.org/10.1155/2011/571795 |
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AT zdeneksmarda boundsofsolutionsofintegrodifferentialequations |
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1725352279796613120 |