Sufficient Conditions for Nonoscillation of Delay Differential Equations with Positive and Negative Coefficients using Schauder’s Fixed Point Theorem

Abstract

Schauder’s fixed point theorem and its applications to delay differential equations (DDEs) cannot be over emphasized. In this work,  interesting results regarding the sufficient conditions for nonoscillation of more generalized forms of DDEs are established and provides  improvements on the results obtained in the past. However, applying the theorem and the characteristic equation of DDE with constant  coefficients helps to determine those conditions. Lastly, to ascertain a claim from an existing literature for a solution that is on oscillatory  and has such larger solutions, comparison theorem is used and the results are found to be true.