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中文摘要：
利用王克发展的内凸紧集法,研究了一类具有无限时滞积微分方程的周期解的存在性.在王克所研究的Volterra型积微分方程的基础上,本文将王克所选取的相空间Ch空间替换为Arino,Burton和Haddock建立的相空间Cg空间,以王克在文献建立的引理为基础,在适当的条件下,得到无限时滞Volterra型积微分方程存在周期解的主要结论。研究表明：由于不同作者所选取的相空间不同,所以,得到的条件也会不同,但是,他们所得结论却相同：即在不同的相空间下,具无限时滞的积微分方程在凸紧集S0中存在一个周期解。文章的结果与王克在文献[2]所得的结果互不包含。
英文摘要：
By using of the interior convex compact set method developed by Wang Ke,the existence of the periodic solution of Volterra type integrodifferential equation with infinite delay is investigated in this paper.Basing on the integrodifferential equation which studied by Wang Ke,we replace the phase space Ch of paper by the phase space Cg which was built by Arino,Burton and Haddock.By the known lemma of paper and some suitable conditions,the existence of the periodic solution for Volterra type integrodifferential equation with infinite delay at the phase space Cg is obtained.Our investigation shows that,the different authors will choose different phase spaces,then the conditions given by different authors are different,although the results obtained by different authors are the same,that is,the integrodifferential equation with infinite delay always has a periodic solution in the convex compact set S0 at different phase spaces.Our results and the results obtained by Wang Ke in paper [2] are non-inclusive each other.
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