微分方程各类解的存在问题是微分方程的一个重要研究方向,概自守函数在微分方程中的应用非常广泛.为了研究紧概自守函数在一类发展微分方程中的应用,利用发展系统的算子半群理论和泛函分析稳定点定理的相关知识,在非李普希兹条件下,研究这类方程在Banach空间中的紧概自守解的存在性和唯一性.研究表明:在非李普希兹条件下,证明了发展方程紧概自守温和解的存在性和唯一性.%This paper building on the insight that the problem of the existence of various solutions re-presents an important direction and almost automorphic functions have a wide application in equations is motivated by the need for to investigate the application of compact almost automorphic functions in some evolution equations.The investigation involves applying the theory of semigroups of operators to evolution family and fixed point theorem, under non-Lipschitz conditions and thereby identifying the existence and uniquencess theorem of compact almost automorphic solutions to the equation in Banach space.The re-sults point to the existence and uniqueness theorem of compact almost automorphic mild solutions of the development equation under non-Lipschitz condition.
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