We study a class of abstract Cauchy problems for semilinear nonautonomous evolution equations involving nonlocal initial conditions. Combining the theory of evolution families with the Krasnosel’skii fixed-point theorem and a decomposition technique, we prove the existence of asymptotically periodic mild solutions to these problems. Our results generalize and improve some previous results, since the condition of (local) Lipschitz continuity of the nonlinearity is not required. A partial differential equation is also presented as an application.
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Published in Neliniini Kolyvannya, Vol. 16, No. 1, pp. 14–28, January–March, 2013.
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Wang, RN., Xiang, QM. & Zhou, Y. Asymptotically Periodic Solutions to Nonlocal Cauchy Problems Governed by Compact Evolution Families. J Math Sci 197, 13–28 (2014). https://doi.org/10.1007/s10958-014-1698-1
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DOI: https://doi.org/10.1007/s10958-014-1698-1