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

研究了具有时滞的泛函微分方程解、积分微分方程解和Volterra差分方程解的定性性质。应用相空间中泛函微分方程常数变分公式，得到了一个关于微扰方程解的性态的结果。此外，我们还建立了关于非线性泛函微分方程解的几个不变流形存在性的结果。此外，我们主要研究了积分微分方程解的正性，得到了正方程稳定性的一个判据。

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.