Systems of Functional Differential Equations on Finite Intervals

Abstract

In Chap. 16, boundary value problems for system of linear functional differential equations are studied, and results on positivity of Green’s matrices are obtained. A necessary and sufficient condition for nonnegativity of all the entries of the Cauchy matrix for linear systems of ordinary differential equations of the first order (obtained by Wazewski) is nonpositivity of off-diagonal coefficients. In the first part of this chapter, extension of this result to various boundary value problems for functional differential equations is obtained, and all the results include an analogue of Wazewski’s sign condition.