Oscillation Of Systems Of Functional Partial Differential Equations

In the last several decades, a lot of scholars made a great deal of work in the study of oscillatory theory of functional partial differential equations and obtained many results. But the research concerning oscillatory property of solutions to systems of functional partial differential equations is still seldom. In this paper, we discuss oscillatory property of systems of functional partial differential equations. We use the averaging technique and Green's formula in order to obtain some necessary or sufficient conditions for oscillation of solutions to systems of functional partial differential equations subject to boudary condition of homogeneous Neumann type; we show the difference between oscillatory property of systems of functional partial differential equations and that of systems of partial differential equations.The paper consists of four chapters:In chaper 1, we introduce the background and signficance, research and actuality on oscillation of functional partial differential equations; we present research subject in this paper;In chaper 2, we discuss oscillatory property of systems of parabolic differential equations with delays and obtain necessary and sufficient conditions for the oscillation of their solutions; we show the difference between oscillatory property of systems of parabolic differential equations with delays and that of systems of partial differential equtions without delays; we explain the main results with examples;In chapter 3, we discuss oscillatory property of systems of functional parabolic differential equations of neutral type; we obtain some sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples;In chapter 4, we discuss oscillatory property of systems of functional hyperbolic differential equations of neutral type; we obtain sufficient conditions for the oscillation or full oscillation of their solutions under some conditions; we explain the main results with examples.