Oscillation Property Of Solutions Of Partial Functional Differential Equations

In recent years,with the development of modern science and technology, people have proposed a great many new problems about partial functional differential equations in natural science and social science,such as mechanics, biology heredity engineering, cybernetics and medicine and so on, which needed us to research them with related mathematical theories. Since the oscillation theory of partial functional differential equation is one of the central contents of the qualitative theory of partial functional differential equation, it is of great theoretical significance and practical value to research the oscillatory properties.The oscillation and the forced oscillation of parabolic partial functional differential equations of neutral type, systems of hyperbolic and higher order partial functional differential equations, impulsive partial functional differential equations are researched.Firstly, oscillatory properties of solutions of certain parabolic partial functional differential equations of neutral type with delay are researched, a series of sufficient and necessary conditions for oscillations of the solutions are established. These results are illustrated by examples.Secondly, some sufficient and necessary conditions for a class of systems of parabolic partial functional differential equations are obtained. These result are explained by examples.Forced oscillation of systems of quasilinear neutral hyperbolic partial functional differential equations are studied by using the method of differential inequality.A class of high-order nonlinear neutral systems of partial functional differential equations with continuous distribution delay is studied. The sufficient conditions are given for the forced oscillation and strong oscillation of systems under some boundary conditions. These results generalize the correspo- nding known results.Finally, the oscillations for impulsive partial functional differential equatio- ns are investigated. By transforming the oscillation problem to the one that the impulsive delayed ordinary differential inequalities don't exist the eventual positive solutions and using impulsive differential inequalities, some oscillatory criteria of impulsive parabolic and hyperbolic equations under the corresponding boundary conditions are obtained.