Oscillation of Nonlinear Hyperbolic Equation with Impulses

Theory of impulsive partial differential equations can be applied to many fields, such as to biology, population growth, engineering, generic repression, control theory and climate model. In the last few years, the fundamental theory of partial differential equations with impulses has undergone intensive development. The qualitative theory of this class of equations, however, is still in an initial stage of development. We may easily visualize situations in nature where abrupt change such as shock and disasters may occur. These phenomena are short-time perturbations whose duration is negligible in comparison with the duration of the whole evolution process. Consequently, it is natural to assume, in modeling these problems, that these perturbations act instantaneously, that is, in the form of impulses. In 1991, the first paper [1] on this class of equations was published. But for instance, only a few papers have been published on oscillation theory of impulsive partial differential equations. Recently, Bainov, Minchev, Luo and Liu[2-7] investigated the oscillation of solutions of impulsive partial differential equations.