Nonoscillation interval for nth order functional differential equations

Nonoscillation plays an important role in the theory of ordinary differential equations, but for functional differential equations and their important class such as delay differential equations, nonoscillation is defined only as the existence of an eventually positive solution on the semiaxis and cannot be used in the analysis of boundary value problems. The use of Azbelev's definition of homogeneous equations allows us to deal with the standard notion of the nonoscillation interval and to obtain results about the existence and uniqueness of the solutions for the interpolation boundary value problems and sign behavior of their Green's functions.