With Continuous Time Delay Nonlinear Differential Equations Of The Study

The theory of functional differential equations is an important branch of the research area of differential equations, which is called FDE or DDE for short. The systematic researches in this field and its applications began at the end of 1940's. So far there are many valuable monographs. The theory is widely used in biology, physics, control theory and engineering problems. In the recent years oscillation for functional differential equations has drawn increasing attention. A great number of research results in this direction have been abtained. In this paper, we study oscillation for three different kinds of delay differential equations of the form.(1) nonlinear neutral hyperbolic equation with continuously distributed time delaywith boundary condition(2) higher order nonlinear neutral delay differential equation(3) second order nonlinear neutral delayed differential equationBy using Green formula, Riccati transformation. Jansen inequality, method of Philos'integral average and Kiguradgze Lemma, we deal with the above difficult problems,establish oscillation criteria for them and generalize existing known results.