Qualitative properties of difference equations and its applications

Abstract

The core of the thesis focuses on the Qualitative properties of newlinesolutions of Riccati Difference equation concur with Riccati transformation newlinetechnique. Oscillation is one of the most prominent and fascinating topics in newlinethe field of qualitative properties of solutions of difference equations. newlineOver the last few decades, there has been active research towards the newlineanalysis of the solutions of equations using and#8710;. Nevertheless, the same analysis newlinefor difference equations associated with and#8710; newline` newlineand and#8710; newlineand#945;(`) newlineis infrequent. In recent years, newlinethe study of resolving Riccati Difference equations for optimal control problems newlinehas risen as a distinct area of modern research. newlineThe current study is divided into seven chapters that discuss the newlineoscillatory and non-oscillatory properties of different classifications of neutral newlinedelay difference equations, as well as other qualitative properties such as newlineboundedness, monotonicity, and convergence of solutions. newlineChapter 1 is an introductory chapter that provides an overview of newlinethe work incorporated in the thesis and intends to provide basic definitions, newlinepreliminary lemmas, and notations that will be required in the following newlinechapters. newlineIn Chapter 2, the Oscillatory properties for the third-order nonlinear newlineneutral distributed delay generalized difference equation of the form newline