Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions
Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u′(t)=Au(t)+∫0tB(t-s)u(s)ds+f(t,u(t)), t∈[0,1], u(0)=g(u), where A:D(A)⊆X→X, and for every t∈[0,1] the...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/647103 |
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| author | Carlos Lizama Juan C. Pozo |
| author_facet | Carlos Lizama Juan C. Pozo |
| author_sort | Carlos Lizama |
| collection | DOAJ |
| description | Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u′(t)=Au(t)+∫0tB(t-s)u(s)ds+f(t,u(t)), t∈[0,1], u(0)=g(u), where A:D(A)⊆X→X, and for every t∈[0,1] the maps B(t):D(B(t))⊆X→X are linear closed operators defined in a Banach space X. We assume further that D(A)⊆D(B(t)) for every t∈[0,1], and the functions f:[0,1]×X→X and g:C([0,1];X)→X are X-valued functions which satisfy appropriate conditions. |
| format | Article |
| id | doaj-art-37b55e11dd5e45f389222487a51a7422 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-37b55e11dd5e45f389222487a51a74222025-02-03T05:58:36ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/647103647103Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial ConditionsCarlos Lizama0Juan C. Pozo1Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago 9160000, ChileFacultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago 7810000, ChileUsing Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions u′(t)=Au(t)+∫0tB(t-s)u(s)ds+f(t,u(t)), t∈[0,1], u(0)=g(u), where A:D(A)⊆X→X, and for every t∈[0,1] the maps B(t):D(B(t))⊆X→X are linear closed operators defined in a Banach space X. We assume further that D(A)⊆D(B(t)) for every t∈[0,1], and the functions f:[0,1]×X→X and g:C([0,1];X)→X are X-valued functions which satisfy appropriate conditions.http://dx.doi.org/10.1155/2012/647103 |
| spellingShingle | Carlos Lizama Juan C. Pozo Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions Abstract and Applied Analysis |
| title | Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions |
| title_full | Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions |
| title_fullStr | Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions |
| title_full_unstemmed | Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions |
| title_short | Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions |
| title_sort | existence of mild solutions for a semilinear integrodifferential equation with nonlocal initial conditions |
| url | http://dx.doi.org/10.1155/2012/647103 |
| work_keys_str_mv | AT carloslizama existenceofmildsolutionsforasemilinearintegrodifferentialequationwithnonlocalinitialconditions AT juancpozo existenceofmildsolutionsforasemilinearintegrodifferentialequationwithnonlocalinitialconditions |