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.
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
.
DOI: 10.1007/s10473-021-0206-1
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