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标题：Existence and Global Asymptotical Stability of Periodic Solution for the <svg style="vertical-align:-0.0pt;width:16.0375px;" id="M1" height="14.7625" version="1.1" viewBox="0 0 16.0375 14.7625" width="16.0375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7625)"> <g transform="translate(72,-60.19)"> <text transform="matrix(1,0,0,-1,-71.95,60.24)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑇</tspan> </text> </g> </g> </svg>-Periodic logistic System with Time-Varying Generating Operators and <svg style="vertical-align:-4.67648pt;width:20.924999px;" height="20.5875" version="1.1" viewBox="0 0 20.924999 20.5875" width="20.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.5875)"> <g transform="translate(72,-55.53)"> <text transform="matrix(1,0,0,-1,-71.95,60.24)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑇</tspan> </text> <text transform="matrix(1,0,0,-1,-62.09,55.76)"> <tspan style="font-size: 12.55px; " x="0" y="0">0</tspan> </text> </g> </g> </svg>-Periodic Impulsive Perturbations on Banach Spaces
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作者：JinRong Wang ; X. Xiang ; W. Wei 等
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2008
卷号：2008
DOI：10.1155/2008/524945
出版社：Hindawi Publishing Corporation
摘要：This paper studies the existence and global asymptotical stability of periodic PC-mild solution for the 𝑇-periodic Logistic system with time-varying generating operators and 𝑇0-periodic impulsive perturbations on Banach spaces. Two sufficient conditions that guarantee the exponential stability of the impulsive evolution operator corresponding to homogenous well-posed 𝑇-periodic system with time-varying generating operators and 𝑇0-periodic impulsive perturbations are given. It is shown that the system have a unique periodic PC-mild solution which is globally asymptotically stable when 𝑇 and 𝑇0 are rational dependent and its period must be 𝑛𝑇0 for some 𝑛∈𝑁. At last, an example is given for demonstration.