The Research On Oscillation Of Solutions To Even Order Neutral Partial Differential Equations With Damping Term

In this dissertation, oscillatory properties of solutions to even order neutral partial differential equations with damping terms are studied. Some criteria of sufficient conditions for the oscillation of all solutions are obtained under Robin and Dirichlet boundary conditions by Riccati transformation and introducing new functions H (t ,s)andΦ(t ,s,l). This dissertation includes four chapters.Chapter 1 is a brief introduction to the historical background and the significance of the study and the main reserch works. Some notations,definitions and lemmas are listed.Chapter 2 is a study on the oscillatory properties of solutions of even order neutral partial differential equations with damping terms. Firstly, we use Philos integral average method to simplify the problem and process neutral terms through the variable substitution.Secondly we use Green formula and boundary conditions to deal with Laplace operators and turn the partial differential equations into some ordinary differential inequalities.Finally, full square techniques and Riccati transformation as well as some new functions H (t ,s)andΦ(t ,s,l) are used to process the damping terms. Some criteria of sufficient conditions for the oscillation of all solutions are obtained.Chapter 3 is a study on the oscillatory properties of solutions of even order neutral partial nonlinear differential equations with damping terms. On the basis of the second chapter,we study the oscillatory properties of solutions of even order neutral partial nonlinear differential equations with damping terms.we use the assumptions and Jensen's inequality to deal with nonlinear terms. Some criteria of sufficient conditions for the oscillation of all solutions are obtained.Chapter 4 is a study on the oscillatory properties of solutions for even order neutral partial differential equations with damping terms and continuously distributed delays. In the second chapter and the third chapter,we study the oscillatory properties of solutions of even order neutral damped partial differential equations with discrete delays.In this chapter ,we study the oscillatory properties of solutions for even order neutral damped partial differential equations with continuously distributed delays. Some criteria of sufficient conditions for the oscillation of all solutions are obtained.