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Weighted pseudo asymptotically periodic mild solutions of evolution equations

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Abstract

In this paper, we propose a new class of functions called weighted pseudo S-asymptotically periodic function in the Stepanov sense and explore its properties in Banach space including composition theorems. Furthermore, the existence, uniqueness of the weighted pseudo S-asymptotically periodic mild solutions to partial evolution equations and nonautonomous semilinear evolution equations are investigated. Some interesting examples are presented to illustrate the main findings.

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Authors and Affiliations

  1. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, P. R. China

    Zhi Nan Xia

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  1. Zhi Nan Xia
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Correspondence to Zhi Nan Xia.

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Supported by National Natural Science Foundation of China (Grant Nos. 11426201, 11271065) and Natural Science Foundation of Zhejiang Province (Grant No. LQ13A010015)

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Xia, Z.N. Weighted pseudo asymptotically periodic mild solutions of evolution equations. Acta. Math. Sin.-English Ser. 31, 1215–1232 (2015). https://doi.org/10.1007/s10114-015-4727-1

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