论文标题
一类抽象延迟微分方程在太阳和恒星的光线下。 ii
A class of abstract delay differential equations in the light of suns and stars. II
论文作者
论文摘要
作者最近在ARXIV中的工作：1901.11526关于一类抽象延迟微分方程（DDE），以及Diekmann和Gyllenberg对其他延迟方程式的早期工作，激励了给定的$ \ nath $ \ nath $ \ banace $ s $ s的一般概念，并引入了可允许的范围和可理关系的空间。相对于$ t_0 $，$ x $不认为是太阳反射。我们调查了$ t_0 $的可接受范围与$ x^{\ odot \ star} $的$ x^{\ odot \ times} $之间的可接受范围之间的关系。我们回答了两个有关可接受性在有限线性扰动方面的鲁棒性的问题，我们使用这些答案来研究半线性问题及其线性化。部分是作为到目前为止开发的材料的应用，部分是作为以抽象DDES形式的模型中现有作品的正当理由，我们比较了非阳性反射案例中中心歧管与Diekmann和van Gils在Sun-Reflexive案例中的已知结果的构建。我们表明，系统的系统使用$ x^{\ odot \ times} $促进了现有结果的概括，而努力相对较少。在这种情况下，我们还为存在$ x $和$ x^{\ odot \ times} $的适当光谱分解提供了足够的条件，而无需假设线性化的半速度最终是紧凑的。然后，作为一个特定情况，一个激励级别的抽象DDE类别的中心歧管定理。
Recent work in arXiv:1901.11526 by the author about a class of abstract delay differential equations (DDEs), as well as earlier work by Diekmann and Gyllenberg on other classes of delay equations, motivates the introduction of the general notion of an admissible range and an admissible perturbation for a given $\mathcal{C}_0$-semigroup $T_0$ on a Banach space $X$ that is not assumed to be sun-reflexive with respect to $T_0$. We investigate the relationship between admissible ranges for $T_0$ and the subspace $X^{\odot\times}$ of $X^{\odot\star}$ introduced by Van Neerven. We answer two questions about robustness of admissibility with respect to bounded linear perturbations and we use these answers to study the semilinear problem and its linearization. Partly as an application of the material developed up to that point, and partly as a justification of existing work on local bifurcations in models taking the form of abstract DDEs, we compare the construction of center manifolds in the non-sun-reflexive case with known results by Diekmann and Van Gils for the sun-reflexive case. We show that a systematic use of the space $X^{\odot\times}$ facilitates a generalization of the existing results with relatively little effort. In this context we also give sufficient conditions for the existence of appropriate spectral decompositions of $X$ and $X^{\odot\times}$ without assuming that the linearized semiflow is eventually compact. A center manifold theorem for the motivating class of abstract DDEs then follows as a particular case.
