Study of stability properties for positive linear equations with delay and related topics

研究了时滞方程中的典型泛函微分方程、积分微分方程和沃尔泰拉差分方程解的定性性质。应用泛函微分方程相空间中的常数变分公式，得到了关于带扰动的方程解的性质的一个结果。同时，我们建立了非线性泛函微分方程几个不变流形存在性的一个结果。进一步，主要以积分微分方程为例，研究了方程的正性，得到了正方程稳定性的一个判别准则。

We studied qualitative properties of solutions in functional differential equations, integrodifferential equations and Volterra difference equations which are typical ones of equations with delay. Applying the variation-of-constants formula in the phase space for functional differential equations, we obtained a result on the behavior of solutions for equations with a perturbation. Also, we established a result on the existence of several invariant manifolds for nonlinear functional differential equations. Furthermore, treating integrodifferential equations mainly, we investigated the positivity of equations, and obtained a criterion on stabilities for positive equations.