Conditions are derived of the existence of solutions of nonlinear boundary-value problems for systems of ordinary differential equations with constant coefficients and single delay (in the linear part) and with a finite number of measurable delays of argument in nonlinearity: , , assuming that these solutions satisfy the initial and boundary conditions if , . The use of a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led 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 ) does not coincide with the number of unknowns in the differential system with a single delay.
A. Boichuk. J. Diblík. D. Khusainov. M. Růžičková. "Boundary-Value Problems for Weakly Nonlinear Delay Differential Systems." Abstr. Appl. Anal. 2011 (SI1) 1 - 19, 2011. https://doi.org/10.1155/2011/631412