Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces
This paper deals with the existence and uniqueness of mild solutions for the initial value problems of abstract impulsive evolution equations in an ordered Banach space E:u′(t)+Au(t)=f(t,u(t),Gu(t)), t∈[0,a], t≠tk, Δu|t=tk=Ik(u(tk)), 0<t1<t2<⋯<tm<a, u(0)=u0, where A:D(A)⊂E→E is a clos...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/481648 |
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| author | He Yang |
| author_facet | He Yang |
| author_sort | He Yang |
| collection | DOAJ |
| description | This paper deals with the existence and uniqueness of mild solutions for the initial value problems of abstract impulsive evolution equations in an ordered Banach space E:u′(t)+Au(t)=f(t,u(t),Gu(t)), t∈[0,a], t≠tk, Δu|t=tk=Ik(u(tk)), 0<t1<t2<⋯<tm<a, u(0)=u0, where A:D(A)⊂E→E is a closed linear operator, and f:[0,a]×E×E→E is a nonlinear mapping. Under wide monotone conditions and measure of noncompactness conditions of nonlinearity f, some existence and uniqueness results are obtained by using a monotone iterative technique in the presence of lower and upper solutions. |
| format | Article |
| id | doaj-art-d82a6eedfa9143e09ca7631d71db2344 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d82a6eedfa9143e09ca7631d71db23442025-02-03T01:02:26ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/481648481648Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach SpacesHe Yang0Department of Mathematics, Northwest Normal University, Lanzhou 730070, ChinaThis paper deals with the existence and uniqueness of mild solutions for the initial value problems of abstract impulsive evolution equations in an ordered Banach space E:u′(t)+Au(t)=f(t,u(t),Gu(t)), t∈[0,a], t≠tk, Δu|t=tk=Ik(u(tk)), 0<t1<t2<⋯<tm<a, u(0)=u0, where A:D(A)⊂E→E is a closed linear operator, and f:[0,a]×E×E→E is a nonlinear mapping. Under wide monotone conditions and measure of noncompactness conditions of nonlinearity f, some existence and uniqueness results are obtained by using a monotone iterative technique in the presence of lower and upper solutions.http://dx.doi.org/10.1155/2010/481648 |
| spellingShingle | He Yang Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces Abstract and Applied Analysis |
| title | Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces |
| title_full | Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces |
| title_fullStr | Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces |
| title_full_unstemmed | Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces |
| title_short | Monotone Iterative Technique for the Initial Value Problems of Impulsive Evolution Equations in Ordered Banach Spaces |
| title_sort | monotone iterative technique for the initial value problems of impulsive evolution equations in ordered banach spaces |
| url | http://dx.doi.org/10.1155/2010/481648 |
| work_keys_str_mv | AT heyang monotoneiterativetechniquefortheinitialvalueproblemsofimpulsiveevolutionequationsinorderedbanachspaces |