Existence Theorem for Noninstantaneous Impulsive Evolution Equations
In this note, the variational form of the classical Lax–Milgram theorem is used for the divulgence of variational structure of the first-order noninstantaneous impulsive linear evolution equation. The existence and uniqueness of the weak solution of the problem is obtained. In future, this construct...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5539306 |
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| _version_ | 1832546067503120384 |
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| author | Gul I Hina Aslam Amjad Ali Maimona Rafiq |
| author_facet | Gul I Hina Aslam Amjad Ali Maimona Rafiq |
| author_sort | Gul I Hina Aslam |
| collection | DOAJ |
| description | In this note, the variational form of the classical Lax–Milgram theorem is used for the divulgence of variational structure of the first-order noninstantaneous impulsive linear evolution equation. The existence and uniqueness of the weak solution of the problem is obtained. In future, this constructive theory can be used for the corresponding semilinear problems. |
| format | Article |
| id | doaj-art-80967956c6bd4cde96fd13f48708e53e |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-80967956c6bd4cde96fd13f48708e53e2025-02-03T07:24:00ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55393065539306Existence Theorem for Noninstantaneous Impulsive Evolution EquationsGul I Hina Aslam0Amjad Ali1Maimona Rafiq2Pakistan Navy Engineering College, National University of Sciences and Technology, Karachi, PakistanFaculty of Science and Technology, University of Debrecen, Debrecen, HungaryDepartment of Mathematics, Comsats University Islamabad, Attock 43600, PakistanIn this note, the variational form of the classical Lax–Milgram theorem is used for the divulgence of variational structure of the first-order noninstantaneous impulsive linear evolution equation. The existence and uniqueness of the weak solution of the problem is obtained. In future, this constructive theory can be used for the corresponding semilinear problems.http://dx.doi.org/10.1155/2021/5539306 |
| spellingShingle | Gul I Hina Aslam Amjad Ali Maimona Rafiq Existence Theorem for Noninstantaneous Impulsive Evolution Equations Journal of Mathematics |
| title | Existence Theorem for Noninstantaneous Impulsive Evolution Equations |
| title_full | Existence Theorem for Noninstantaneous Impulsive Evolution Equations |
| title_fullStr | Existence Theorem for Noninstantaneous Impulsive Evolution Equations |
| title_full_unstemmed | Existence Theorem for Noninstantaneous Impulsive Evolution Equations |
| title_short | Existence Theorem for Noninstantaneous Impulsive Evolution Equations |
| title_sort | existence theorem for noninstantaneous impulsive evolution equations |
| url | http://dx.doi.org/10.1155/2021/5539306 |
| work_keys_str_mv | AT gulihinaaslam existencetheoremfornoninstantaneousimpulsiveevolutionequations AT amjadali existencetheoremfornoninstantaneousimpulsiveevolutionequations AT maimonarafiq existencetheoremfornoninstantaneousimpulsiveevolutionequations |