We propose an approach for studying positivity of Green’s operators of a nonlocal boundary value problem for the system of $n$ linear functional differential equations with the boundary conditions $n_i{x}_i-{\sum }_{j=1}^n{m}_{ij}{x}_j={\beta }_i$, $i=1,\cdots ,n$, where $n_i$ and $m_{ij}$ are linear bounded “local” and “nonlocal“ functionals, respectively, from the space of absolutely continuous functions. For instance, $n_i{x}_i=x_i\left(\omega \right)$ or $n_i{x}_i=x_i\left(0\right)-x_i\left(\omega \right)$ and $m_{ij}{x}_j={\int }_0^{\omega }k\left(s\right)x_j\left(s\right)\mathrm{d}s+{\sum }_{r=1}^{n_{ij}}{c}_{ijr}{x}_j\left(t_{ijr}\right)$ can be considered. It is demonstrated that the positivity of Green’s operator of nonlocal problem follows from the positivity of Green’s operator...

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $$\dot{x}\left(t\right)+\sum _{k=1}^m{a}_k\left(t\right)x\left(h_k\left(t\right)\right)=0,a_k\left(t\right)\ge 0$$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.