Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions
In this paper we prove the existence of a mild solution for a semilinear evolution differential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator gen...
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| Format: | Article |
| Language: | English |
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Texas State University
2009-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2009/42/abstr.html |
| _version_ | 1818235367038386176 |
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| author | Reem A. Al-Omair Ahmed G. Ibrahim |
| author_facet | Reem A. Al-Omair Ahmed G. Ibrahim |
| author_sort | Reem A. Al-Omair |
| collection | DOAJ |
| description | In this paper we prove the existence of a mild solution for a semilinear evolution differential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator generated by the family operators. Also, we prove that the set of mild solutions is compact. |
| first_indexed | 2024-12-12T11:52:50Z |
| format | Article |
| id | doaj.art-0591c03a40c643e5b2b9c87eae6ba986 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T11:52:50Z |
| publishDate | 2009-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-0591c03a40c643e5b2b9c87eae6ba9862022-12-22T00:25:16ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912009-03-01200942,111Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditionsReem A. Al-OmairAhmed G. IbrahimIn this paper we prove the existence of a mild solution for a semilinear evolution differential inclusion with nonlocal condition and governed by a family of linear operators, not necessarily bounded or closed, in a Banach space. No compactness assumption is assumed on the evolution operator generated by the family operators. Also, we prove that the set of mild solutions is compact.http://ejde.math.txstate.edu/Volumes/2009/42/abstr.htmlEvolution operatorgeneralized Cauchy operatormeasure of noncompactnessdifferential inclusionsnonlocal conditionsmild solutions |
| spellingShingle | Reem A. Al-Omair Ahmed G. Ibrahim Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions Electronic Journal of Differential Equations Evolution operator generalized Cauchy operator measure of noncompactness differential inclusions nonlocal conditions mild solutions |
| title | Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions |
| title_full | Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions |
| title_fullStr | Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions |
| title_full_unstemmed | Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions |
| title_short | Existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions |
| title_sort | existence of mild solutions of a semilinear evolution differential inclusions with nonlocal conditions |
| topic | Evolution operator generalized Cauchy operator measure of noncompactness differential inclusions nonlocal conditions mild solutions |
| url | http://ejde.math.txstate.edu/Volumes/2009/42/abstr.html |
| work_keys_str_mv | AT reemaalomair existenceofmildsolutionsofasemilinearevolutiondifferentialinclusionswithnonlocalconditions AT ahmedgibrahim existenceofmildsolutionsofasemilinearevolutiondifferentialinclusionswithnonlocalconditions |