Estimation of the growth and study of the oscillation of solutions of complex differential equations and complex difference equations

Abstract

Understanding the growth and oscillation of solutions to differential equations, difference equations and delay-differential equations, is crucial for predicting their behavior. Nevanlinna theory, with its deep insight into the value distribution of meromorphic functions, provides a powerful framework for analyzing the growth and oscillation of solutions to these equations. In this thesis, by using this theory, we present some results regarding the growth and oscillation of solutions of linear differential equations with analytic or meromorphic coefficients in the extended complex plane except at a finite isolated point, we also discuss some results on the growth of solutions of linear difference equations and linear delay-differential equations , in which the coefficients are meromorphic functions in the complex plane.