Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces
We prove two existence theorems for the integrodifferential equation of mixed type: x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds), x(0)=x0, where in the first part of this paper f, g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Hensto...
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| Format: | Article |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/65947 |
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| author | Aneta Sikorska-Nowak Grzegorz Nowak |
| author_facet | Aneta Sikorska-Nowak Grzegorz Nowak |
| author_sort | Aneta Sikorska-Nowak |
| collection | DOAJ |
| description | We prove two existence theorems for the integrodifferential equation of mixed type: x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds), x(0)=x0, where in the first part of this paper f, g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functions f, g, h, x satisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness. |
| format | Article |
| id | doaj-art-2987084fe0ee4e648cb74d5c564d5f7c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2987084fe0ee4e648cb74d5c564d5f7c2025-02-03T01:07:48ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/6594765947Nonlinear Integrodifferential Equations of Mixed Type in Banach SpacesAneta Sikorska-Nowak0Grzegorz Nowak1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Poznań 61-614, PolandUniversity of Marketing and Management, Ostroroga 9a, Leszno 64-100, PolandWe prove two existence theorems for the integrodifferential equation of mixed type: x'(t)=f(t,x(t),∫0tk1(t,s)g(s,x(s))ds,∫0ak2(t,s)h(s,x(s))ds), x(0)=x0, where in the first part of this paper f, g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f, g, h, x are weakly-weakly sequentially continuous functions and integrals are taken in the sense of Henstock-Kurzweil-Pettis (HKP) integral. Additionally, the functions f, g, h, x satisfy some conditions expressed in terms of the measure of noncompactness or the measure of weak noncompactness.http://dx.doi.org/10.1155/2007/65947 |
| spellingShingle | Aneta Sikorska-Nowak Grzegorz Nowak Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces International Journal of Mathematics and Mathematical Sciences |
| title | Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces |
| title_full | Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces |
| title_fullStr | Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces |
| title_full_unstemmed | Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces |
| title_short | Nonlinear Integrodifferential Equations of Mixed Type in Banach Spaces |
| title_sort | nonlinear integrodifferential equations of mixed type in banach spaces |
| url | http://dx.doi.org/10.1155/2007/65947 |
| work_keys_str_mv | AT anetasikorskanowak nonlinearintegrodifferentialequationsofmixedtypeinbanachspaces AT grzegorznowak nonlinearintegrodifferentialequationsofmixedtypeinbanachspaces |