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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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2013
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| Series: | Нелінійні коливання |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/177037 |
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| Summary: | 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. |
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