S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

doi:10.1007/s10473-021-0206-1

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (2): 413-425.doi: 10.1007/s10473-021-0206-1

S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

常永奎, 魏艳艳

School of Mathematics and Statistics, Xidian University, Xi'an 710071, China

收稿日期:2019-10-08 修回日期:2020-10-26 出版日期:2021-04-25 发布日期:2021-04-29
作者简介:Yong-Kui CHANG,E-mail:ykchang@xidian.edu.cn,lzchangyk@163.com; Yanyan WEI,E-mail:yywei@stu.xidian.edu.cn
基金资助:
This work was partially supported by NSF of Shaanxi Province (2020JM-183).

S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

Yong-Kui CHANG, Yanyan WEI

School of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Received:2019-10-08 Revised:2020-10-26 Online:2021-04-25 Published:2021-04-29
About author:Yong-Kui CHANG,E-mail:ykchang@xidian.edu.cn,lzchangyk@163.com; Yanyan WEI,E-mail:yywei@stu.xidian.edu.cn
Supported by:
This work was partially supported by NSF of Shaanxi Province (2020JM-183).

摘要/Abstract

摘要： This paper is mainly concerned with the $S$-asymptotically Bloch type periodicity. Firstly, we introduce a new notion of $S$-asymptotically Bloch type periodic functions, which can be seen as a generalization of concepts of $S$-asymptotically $\omega$-periodic functions and $S$-asymptotically $\omega$-anti-periodic functions. Secondly, we establish some fundamental properties on $S$-asymptotically Bloch type periodic functions. Finally, we apply the results obtained to investigate the existence and uniqueness of $S$-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.

关键词: S-asymptotically Bloch type periodic functions, S-asymptotically ω antiperiodic functions, evolution equations

Abstract: This paper is mainly concerned with the $S$-asymptotically Bloch type periodicity. Firstly, we introduce a new notion of $S$-asymptotically Bloch type periodic functions, which can be seen as a generalization of concepts of $S$-asymptotically $\omega$-periodic functions and $S$-asymptotically $\omega$-anti-periodic functions. Secondly, we establish some fundamental properties on $S$-asymptotically Bloch type periodic functions. Finally, we apply the results obtained to investigate the existence and uniqueness of $S$-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.

Key words: S-asymptotically Bloch type periodic functions, S-asymptotically ω antiperiodic functions, evolution equations

中图分类号:

34C25

常永奎, 魏艳艳. S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES[J]. 数学物理学报(英文版), 2021, 41(2): 413-425.

Yong-Kui CHANG, Yanyan WEI. S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES[J]. Acta mathematica scientia,Series B, 2021, 41(2): 413-425.

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S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

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