Oscillation Of Solutions For Some Differential Equations With Deviating Arguments

With the increasing development of natural science, in the field of natural science including physics, theory of control, biology, medicine, economies and edging field, many mathematical models which are described by differential equations are proposed. Differential equations are powerful tools that describe the law of nature, but it is difficult to find their general solutions. Therefore, there has been an increasing interest in the study of the nature of solutions of differ-ential equation in theory.This paper will use a variety of known techniques research the oscillation and nonoscilla-tion of differential equations with deviating arguments. This dissertation focuses on two sides: one is the oscillation of ordinary differential equations with deviating arguments, the other is the partial differential equations with deviating arguments. The paper is made up of four chapters. Main contents are as follows:In chapter one, we give a survey to the development and current state of oscillation of or-dinary(partial) differential equations with deviating arguments, as well as the main work status.In chapter two, using some integral operators and generalized Riccati technique, we estab-lish some new oscillation criteria for a second order neutral differential equation with deviating arguments. The obtained results are different from most known ones and can be applied to many cases which are not covered by existing.In chapter three, we consider certain neutral hyperbolic equations with continuous deviat-ing arguments, and sufficient conditions presented for every solution of some boundary value problems under two different cases to be oscillatory in a cylindrical domain.In chapter four, nonoscillation of higher order differential equation with deviating argu-ments depending on the unknown function is consider.