Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption
Abstract In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with nonlocal conditions. Using the Schauder’s fixed-point theorem as well as the theory of evolution family, we prove the existence of mild solutions f...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01819-5 |
| _version_ | 1797349818506412032 |
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| author | Lixin Sheng Weimin Hu You-Hui Su |
| author_facet | Lixin Sheng Weimin Hu You-Hui Su |
| author_sort | Lixin Sheng |
| collection | DOAJ |
| description | Abstract In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with nonlocal conditions. Using the Schauder’s fixed-point theorem as well as the theory of evolution family, we prove the existence of mild solutions for the concerned problem. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. An example is given of the application of the results. |
| first_indexed | 2024-03-08T12:35:57Z |
| format | Article |
| id | doaj.art-e8c1de47b08d42bfa2cc2f4e311c6466 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-03-08T12:35:57Z |
| publishDate | 2024-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-e8c1de47b08d42bfa2cc2f4e311c64662024-01-21T12:28:33ZengSpringerOpenBoundary Value Problems1687-27702024-01-012024111510.1186/s13661-024-01819-5Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumptionLixin Sheng0Weimin Hu1You-Hui Su2School of Mathematics and Statistics, Yili Normal UniversitySchool of Mathematics and Statistics, Yili Normal UniversitySchool of Mathematics and Statistics, Xuzhou University of TechnologyAbstract In this paper, we investigate the existence of mild solutions as well as optimal controls for non-autonomous impulsive evolution equations with nonlocal conditions. Using the Schauder’s fixed-point theorem as well as the theory of evolution family, we prove the existence of mild solutions for the concerned problem. Furthermore, without the Lipschitz continuity of the nonlinear term, the optimal control result is derived by setting up minimizing sequences twice. An example is given of the application of the results.https://doi.org/10.1186/s13661-024-01819-5Impulsive evolution equationOptimal controlsNonlocal conditionsResolvent operatorSchauder’s fixed point theorem |
| spellingShingle | Lixin Sheng Weimin Hu You-Hui Su Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption Boundary Value Problems Impulsive evolution equation Optimal controls Nonlocal conditions Resolvent operator Schauder’s fixed point theorem |
| title | Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption |
| title_full | Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption |
| title_fullStr | Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption |
| title_full_unstemmed | Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption |
| title_short | Existence and optimal controls of non-autonomous for impulsive evolution equation without Lipschitz assumption |
| title_sort | existence and optimal controls of non autonomous for impulsive evolution equation without lipschitz assumption |
| topic | Impulsive evolution equation Optimal controls Nonlocal conditions Resolvent operator Schauder’s fixed point theorem |
| url | https://doi.org/10.1186/s13661-024-01819-5 |
| work_keys_str_mv | AT lixinsheng existenceandoptimalcontrolsofnonautonomousforimpulsiveevolutionequationwithoutlipschitzassumption AT weiminhu existenceandoptimalcontrolsofnonautonomousforimpulsiveevolutionequationwithoutlipschitzassumption AT youhuisu existenceandoptimalcontrolsofnonautonomousforimpulsiveevolutionequationwithoutlipschitzassumption |