Existence and stability of solutions to neutral equations with infinite delay
In this article, by using a fixed point theorem, we study the existence and regularity of mild solutions for a class of abstract neutral functional differential equations with infinite delay. The fraction power theory and alpha-norm is used to discuss the problem so that the obtained results can...
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| Format: | Article |
| Language: | English |
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Texas State University
2013-02-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/55/abstr.html |
| _version_ | 1828951667343622144 |
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| author | Xianlong Fu |
| author_facet | Xianlong Fu |
| author_sort | Xianlong Fu |
| collection | DOAJ |
| description | In this article, by using a fixed point theorem, we study the existence and regularity of mild solutions for a class of abstract neutral functional differential equations with infinite delay. The fraction power theory and alpha-norm is used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. A stability result for the autonomous case is also established. We conclude with an example that illustrates the applications of the results obtained. |
| first_indexed | 2024-12-14T06:41:11Z |
| format | Article |
| id | doaj.art-a855e04dd5064a09a71118628e84a3eb |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T06:41:11Z |
| publishDate | 2013-02-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-a855e04dd5064a09a71118628e84a3eb2022-12-21T23:13:13ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-02-01201355,119Existence and stability of solutions to neutral equations with infinite delayXianlong FuIn this article, by using a fixed point theorem, we study the existence and regularity of mild solutions for a class of abstract neutral functional differential equations with infinite delay. The fraction power theory and alpha-norm is used to discuss the problem so that the obtained results can be applied to equations with terms involving spatial derivatives. A stability result for the autonomous case is also established. We conclude with an example that illustrates the applications of the results obtained.http://ejde.math.txstate.edu/Volumes/2013/55/abstr.htmlNeutral functional differential equationanalytic semigroupfractional power operatorlinearized stabilityinfinite delay |
| spellingShingle | Xianlong Fu Existence and stability of solutions to neutral equations with infinite delay Electronic Journal of Differential Equations Neutral functional differential equation analytic semigroup fractional power operator linearized stability infinite delay |
| title | Existence and stability of solutions to neutral equations with infinite delay |
| title_full | Existence and stability of solutions to neutral equations with infinite delay |
| title_fullStr | Existence and stability of solutions to neutral equations with infinite delay |
| title_full_unstemmed | Existence and stability of solutions to neutral equations with infinite delay |
| title_short | Existence and stability of solutions to neutral equations with infinite delay |
| title_sort | existence and stability of solutions to neutral equations with infinite delay |
| topic | Neutral functional differential equation analytic semigroup fractional power operator linearized stability infinite delay |
| url | http://ejde.math.txstate.edu/Volumes/2013/55/abstr.html |
| work_keys_str_mv | AT xianlongfu existenceandstabilityofsolutionstoneutralequationswithinfinitedelay |