论文标题
在一类延迟的集成差方程
On a class of retarded integrodifferential equations
论文作者
论文摘要
Banach空间中的以下类延迟的integro-差异方程式 \ [ \ dot {x} \ left（t \ right）= ax \ left（t \ right）+\ int_ {0}^{t}^{t} b \ left（t-τ\右） \] 在这项研究中考虑了。该方程式的延迟项$lx_τ$插入了具有标量内核的卷积产品的积分中。我们证明了使用Miyadera-Voigt扰动和半群理论所研究的问题的良好性。我们还探讨了相关的抽象库奇问题的光谱分析。
The following class of retarded integro-differential equations in a Banach space \[ \dot{x}\left(t\right)=Ax\left(t\right)+\int_{0}^{t}b\left(t-τ\right)Lx_τdτ+Kx_{t};\,\,t\geq0, \] are taken into consideration in this study. The delay term $Lx_τ$ of this equation is inserted into the integral as a convolution product with a scalar kernel. We prove the well-posedness of the problem under investigation using the Miyadera-Voigt perturbation and the theory of semigroups. We also explore the spectral analysis of an associated abstract Cauchy problem.
