Delay Hyperbolic Equation Of Second Order Differential Equations With Damping Vibration Criteria

Oscillation theory of functional differential equation is an important branch of the research field of functional differential equations, which has deep backgrounds of applications. It arises in many research areas, such as biology, ecology, physiology physics and so on. In the recent years, the study of oscillation for functional differential equations attracts wide attention and gains rich achievements in scientific research. Most of the results, however, is devoted to equations with discrete delays, while there are few results for ones with continuous distributed delays and second order nonlinear damper differential equations. In this paper, we establish oscillation criteria for these equations, which generalize or improve some existing oscillation theorems (see[1]-[10]). The present paper is divided into four sections.In chapter 1, we introduce the background and present situation of oscillation of functional differential equations.In chapter 2, we introduce methods of H fuction,average thchnique and trasformationof Riccati to study oscillation results of a hyperbolic differential equation with delayIn chapter 3,we study the oscillation for higher order nonlinear partial function differential equation of neutral typeby the way of turning higher order equations into second order ones with H-method.We obtain some oscillation criteria.In chapter 4, we study oscillation results for a second order nonlinear damped differential equationby using average technique.