| Abstrakt: |
Abstract: 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_ix_i-\sum\nolimits_{j=1}^nm_{ij}x_j=\beta_i, i=1,\dots,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_ix_i=x_i(\omega) or $n_ix_i=x_i(0)-x_i(\omega) and m_{ij}x_j=\int_0^{\omega}k(s)x_j(s) d s +\sum\nolimits_{r=1}^{n_{ij}}c_{ijr}x_j(t_{ijr}) can be considered. It is demonstrated that the positivity of Green's operator of nonlocal problem follows from the positivity of Green's operator for auxiliary "local" problem which consists of a "close" equation and the local conditions n_ix_i=\alpha_i, $i=1,\dots,n. |
