文献类型：期刊文献

英文题名：A Class of (omega, T)-Periodic Solutions for Impulsive Evolution Equations of Sobolev Type

作者：Liu, Kui Feckan, Michal Wang, JinRong

第一作者：Liu, Kui;刘葵

通信作者：Wang, JR[1]

机构：[1]Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China;[2]Comenius Univ, Dept Math Anal & Numer Math, Fac Math Phys & Informat, Bratislava 84248, Slovakia;[3]Slovak Acad Sci, Math Inst, Stefinikova 49, Bratislava 81473, Slovakia;[4]Guizhou Inst Technol, Coll Sci, Guiyang 550025, Guizhou, Peoples R China

第一机构：Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China

通信机构：corresponding author), Guizhou Univ, Dept Math, Guiyang 550025, Guizhou, Peoples R China.

年份：0

外文期刊名：BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY

收录：;Scopus(收录号：2-s2.0-85122996104);WOS:【SCI-EXPANDED(收录号:WOS:000742327100001)】；

基金：This work is partially supported by the National Natural Science Foundation of China (12161015), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016), Guizhou Provincial Science and Technology Foundation ([2020]1Y002), Youth Development Project of Guizhou Provincial Education Department ([2021]266); Academic seedling cultivation and innovation exploration special cultivation project plan (GZLGXM-17), the Slovak Research and Development Agency under the Contract no. APVV-18-0308, and the Slovak Grant Agency VEGA no. 1/0358/20 and no. 2/0127/20.

语种：英文

外文关键词：Impulsive evolution systems of Sobolev type; (omega, T)-periodic solutions; Existence and uniqueness

摘要：In this paper, we study a new class of Sobolev type (omega, T)-periodic linear and semilinear impulsive evolution equations, where T denotes a linear isomorphism from Banach space X to itself. We give a sufficient and necessary condition depending on the initial value, periodic boundary value and linear isomorphism to guarantee that the homogeneous linear impulsive problem has a (omega, T)-periodic solution. Next, we give the explicit expression of (omega, T)-periodic solutions for nonhomogeneous linear impulsive problem and derive two important estimations for the certain sum and integration including the Green function. Further, we show the existence and uniqueness of solutions to semilinear impulsive problem, where we remove the compactness of AB(-1) and use the compactness of a mapping depending on the nonlinear term. Finally, examples are provided to illustrate the theoretical results.