A Study on Oscillation Theory of Higher Order Functional Differential and Difference Equations

Abstract

This thesis investigates the oscillatory and asymptotic behavior of all solutions newlineto higher-order functional differential equations. The initial chapter is dedicated to newlinethe necessary introduction and inspiration. In the second chapter, we explore thirdorder newlinequasi-linear differential equations with a superlinear neutral term. We establish newlinea necessary condition for the oscillation of all solutions to this equation. The third newlinechapter discusses a third-order differential equation that includes both positive and newlinenegative term. The fourth chapter focuses on a third-order differential equation with newlinea distributed deviating argument. The fifth chapter summarizes the even order half newlinelinear differential equation, while the sixth chapter illustrates the higher order difference newlineequation with a superlinear neutral term. All of the results are obtained using the riccati newlinetype transformation, the average technique, and inequalities. Additionally, the primary newlineresults are supported by the inclusion of examples for clarification newline