*(English)*Zbl 1222.34075

Summary: Conditions are derived for the existence of solutions to nonlinear boundary-value problems for systems of $n$ ordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of the argument in the nonlinearity:

assuming that these solutions satisfy the initial and boundary conditions

The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices leads to an explicit and analytical form of sufficient conditions for the existence of solutions in a given space and, moreover, to the construction of an iterative process for finding the solutions of such problems in a general case when the number of boundary conditions (defined by a linear vector functional $\ell $) does not coincide with the number of unknowns in the differential system with single delay.

##### MSC:

34K10 | Boundary value problems for functional-differential equations |

34A45 | Theoretical approximation of solutions of ODE |