Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families
This paper is devoted to a study of a class of abstract Cauchy problems for semilinear nonautonomous evolution equations involving nonlocal initial conditions. Combining the theory of evolution families and the fixed point theorem due to Krasnoselskii, as well as a decomposition technique, we prove...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2013 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/177037 |
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| Цитувати: | Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families / R.-N. Wang, Q.-M. Xiang, Y. Zhou // Нелінійні коливання. — 2013. — Т. 16, № 1. — С. 14-28. — Бібліогр.: 25 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-177037 |
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dspace |
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irk-123456789-1770372021-02-11T01:27:47Z Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families Wang, R.-N. Xiang, Q.-M. Zhou, Y. This paper is devoted to a study of a class of abstract Cauchy problems for semilinear nonautonomous evolution equations involving nonlocal initial conditions. Combining the theory of evolution families and the fixed point theorem due to Krasnoselskii, as well as a decomposition technique, we prove the existence of the asymptotically periodic mild solutions to such problems. Our results generalize and improve some previous results since the (locally) Lipschitz continuity on the nonlinearity is not required. A partial differential equation is also presented as an application. Статтю присвячено вивченню класу абстрактних задач Кошi для напiвлiнiйних неавтономних еволюцiйних рiвнянь з нелокальними початковими умовами. З використанням теорiї еволюцiйних сiмей та теореми Красносельського про нерухому точку, а також технiки розкладу доведено iснування асимптотично перiодичних м’яких розв’язкiв таких задач. Наведенi результати узагальнюють та покращують попереднi результати, оскiльки не вимагається, щоб нелiнiйнiсть задовольняла (локальну) умову Лiпшиця. Як приклад наведено диференцiальне рiвняння з частинними похiдними. 2013 Article Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families / R.-N. Wang, Q.-M. Xiang, Y. Zhou // Нелінійні коливання. — 2013. — Т. 16, № 1. — С. 14-28. — Бібліогр.: 25 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/177037 517.9 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
This paper is devoted to a study of a class of abstract Cauchy problems for semilinear nonautonomous evolution equations involving nonlocal initial conditions. Combining the theory of evolution families and the fixed point theorem due to Krasnoselskii, as well as a decomposition technique, we prove the existence of the asymptotically periodic mild solutions to such problems. Our results generalize and improve some previous results since the (locally) Lipschitz continuity on the nonlinearity is not required. A partial differential equation is also presented as an application. |
| format |
Article |
| author |
Wang, R.-N. Xiang, Q.-M. Zhou, Y. |
| spellingShingle |
Wang, R.-N. Xiang, Q.-M. Zhou, Y. Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families Нелінійні коливання |
| author_facet |
Wang, R.-N. Xiang, Q.-M. Zhou, Y. |
| author_sort |
Wang, R.-N. |
| title |
Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families |
| title_short |
Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families |
| title_full |
Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families |
| title_fullStr |
Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families |
| title_full_unstemmed |
Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families |
| title_sort |
asymptotically periodic solutions to nonlocal cauchy problems governed by compact evolution families |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/177037 |
| citation_txt |
Asymptotically periodic solutions to nonlocal Cauchy problems governed by compact evolution families / R.-N. Wang, Q.-M. Xiang, Y. Zhou // Нелінійні коливання. — 2013. — Т. 16, № 1. — С. 14-28. — Бібліогр.: 25 назв. — англ. |
| series |
Нелінійні коливання |
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2023-10-18T22:42:38Z |
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2023-10-18T22:42:38Z |
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1796156230635356160 |