Oscillation Of Solutions To Impulsive Partial Differential Equations With Delay

The oscillation theory for partial differential equations has been developed intensively in the last decades due to its numerous applications in physics, population dynamics, technology, etc. In the present paper, we study the oscillation of solution to impulsive partial differential equations with delay, which can be deduced from the corresponding properties of ordinary differential equations or inequalities. Some sufficient conditions are established.The thesis consists of five chapters:In the first chapter, the background and significance of impulsive ordinary differential equation and the main types of equations in this paper are introduced;In the second chapter, we discuss oscillation of solution to impulsive ordinary differential equations with delay and some sufficient conditions are established;In the third chapter, oscillation of solution to impulsive parabolic differential equations with delay have been studied. A method used to judge whether a solution of partial differential equations oscillate or not is introduced and some sufficient conditions are established.In the fourth chapter, we study oscillation of solution to impulsive hyperbolic differential equations without impulse. Some sufficient conditions are established by using the similar method introduced in the third chapter.In the last chapter, oscillations of a system of hyperbolic equations are deduced from the corresponding properties of an ordinary differential inequalities by using eigen function and Green formula, etc.