Oscillatory Theory Of An Even Order Hyperbolic Equation With Delays

In the last decades, lots of scholars are interesting in the study of oscillatory theory of solutions to differential equations with deviating arguments and obtained many important results. But, the research concerning oscillatory of solutions to countless functional partial differential equations is still seldom. In this paper, we discuss oscillatory property of solutions to an even order functional partial differential equation. We use Green's formula and Jensen inequality in order to get oscillatory property of equations which are discussed in two kinds of boundary conditions.The paper consists of three chapters:In chapter 1, we introduce the background and significance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper.In chapter 2, we discuss oscillatory property of the second order hyperbolic equations with deviating arguments in two kinds of boundary conditions. And we will get many theorems to judge solutions of the equation oscillate or not.In chapter 3, in basis of the second chapter, we discuss the even order equation. And we will get many useful theorems to judge all solutions of the equation oscillate.