Nonoscillatory functional-differential equations

Abstract

Our aim in this paper is to obtain sufficient conditions under which certain functional differential equations have a number of nonoscillatory solutions. Using the characteristic equation of a majorant delay differential equation with constant coefficients and Schauder's fixed point theorem, we obtain conditions under which the functional differential equation in question has a nonoscillatory solution. Then a known comparison theorem is employed as a tool to demonstrate that if the functional differential equation has a nonoscillatory solution, then it really has a large number of such solutions.