Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces
We prove existence theorems for the integrodifferential equation x'(t)=f(t,x(t),∫0tk(t,s, x(s))ds), x(0)=x0, t∈Ia=[0,a], a>0, where f,k,x are functions with values in a Banach space E and the integral is taken in the sense of HL. Additionally, the functions f and k satisfy certain boundary c...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2007/31572 |
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| author | Aneta Sikorska-Nowak |
| author_facet | Aneta Sikorska-Nowak |
| author_sort | Aneta Sikorska-Nowak |
| collection | DOAJ |
| description | We prove existence theorems for the integrodifferential equation x'(t)=f(t,x(t),∫0tk(t,s, x(s))ds), x(0)=x0, t∈Ia=[0,a], a>0, where f,k,x are functions with values in a Banach space E and the integral is taken in the sense of HL.
Additionally, the functions f and k satisfy certain boundary conditions expressed in terms of the measure
of noncompactness. |
| format | Article |
| id | doaj-art-46a5b49b6ef84589ab9011de5509cb10 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-46a5b49b6ef84589ab9011de5509cb102025-02-03T06:07:56ZengWileyJournal of Applied Mathematics1110-757X1687-00422007-01-01200710.1155/2007/3157231572Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach SpacesAneta Sikorska-Nowak0Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, Poznań 61-614, PolandWe prove existence theorems for the integrodifferential equation x'(t)=f(t,x(t),∫0tk(t,s, x(s))ds), x(0)=x0, t∈Ia=[0,a], a>0, where f,k,x are functions with values in a Banach space E and the integral is taken in the sense of HL. Additionally, the functions f and k satisfy certain boundary conditions expressed in terms of the measure of noncompactness.http://dx.doi.org/10.1155/2007/31572 |
| spellingShingle | Aneta Sikorska-Nowak Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces Journal of Applied Mathematics |
| title | Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces |
| title_full | Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces |
| title_fullStr | Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces |
| title_full_unstemmed | Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces |
| title_short | Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces |
| title_sort | existence theory for integrodifferential equations and henstock kurzweil integral in banach spaces |
| url | http://dx.doi.org/10.1155/2007/31572 |
| work_keys_str_mv | AT anetasikorskanowak existencetheoryforintegrodifferentialequationsandhenstockkurzweilintegralinbanachspaces |