Abstract: By using a new technique of treating quasilinear diffusion term and the method of differential inequalities, we discussed the (full) oscillation problems for a class of delay hyperbolic distributed parameter systems with quasilinear diffusion term under homogeneous Neumann boundary value condition. Firstly, the oscillation problems of the systems were transformed into the problems of two order delay differential inequality without eventually position solution, and then some explicit sufficient conditions for the (full) oscillation of each solution of such systems were established by means of some results of the functional differential equations. The obtained results reflected the role of the delay in determining the (full) oscillation of system.

Key words: hyperbolic distributed parameter system, delay, quasilinear diffusion term, (full) oscillation, eventually positive solution