Banach空间中立型泛函微分方程的概周期温和解

Almost periodic mild solutions to functional differential equations of neutral type in Banach space

借助于一般的谱分解技巧,利用线性算子半群理论研究了Banach空间X中立型泛函微分方程一致连续的有界温和解的存在性与唯一性,得到了当X没有与c0同构的子空间时方程概周期温和解存在与唯一的谱条件,推广了线性微分方程的现有结果。

With the general spectral decomposition techniques and by means of the linear operator semigroups theory, the existence and uniqueness of uniformly continuous mild solutions to the functional differential equations of neutral type in Banach space X are studied. The spectrum conditions which imply the existence and uniqueness of almost periodic mild solutions to the equations are obtained when X has no subspace isomorphic to co . The results extend recent results of the linear differential equations.