$ (\omega,\mathbb{T}) $-periodic solutions of impulsive evolution equations

Abstract

<p style='text-indent:20px;'>In this paper, we study <inline-formula><tex-math id="M2">\begin{document}$ (\omega,\mathbb{T}) $\end{document}</tex-math></inline-formula>-periodic impulsive evolution equations via the operator semigroups theory in Banach spaces <inline-formula><tex-math id="M3">\begin{document}$ X $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{T}: X\rightarrow X $\end{document}</tex-math></inline-formula> is a linear isomorphism. Existence and uniqueness of <inline-formula><tex-math id="M5">\begin{document}$ (\omega,\mathbb{T}) $\end{document}</tex-math></inline-formula>-periodic solutions results for linear and semilinear problems are obtained by Fredholm alternative theorem and fixed point theorems, which extend the related results for periodic impulsive differential equations.</p>