Oscillatory And Asymptotic Behavior Of The Solution For Several Types Of The Functional Differential Equations

Functional differential equations are widely used in the real world. Many disciplines in natural science and social science such as circuit signal systems, ecological systems, nuclear physics.genetic problems, capitalist economy cyclical crisis, transportation scheduling problems, commercial sales problems in social science, have put forward a lot of functional differential equations. People found functional differential equations can more accurately describe the objective world than ordinary differential equations. So the research of the functional differential equation is of great importance. Oscillatory and asymptotic behav-ior are the basic problems of functional differential equations, thus it's necessary to study oscillatory and asymptotic behavior of the solution for functional differential equations.The organization of this thesis is as follows.In Part1, we introduce the related research background of functional differential equa-tions and give the necessary preliminary knowledge.In Part2, we give some oscillatory criteria for a kind of second order nonlinear func-tional differential equations with deviating arguments depended on the state, and discuss asymptotic behavior of the boundary oscillatory solution.In Part3, a kind of second-order impulsive nonlinear FDE is studied. By using impul-sive differential inequalities established by Lakshmikantham etc., we give several criteria on the oscillations of solutions. At last, an example is presented to demonstrate our results.In Part4, based on the theory of time scales, we study some oscillatory and asymptotic properties for second-order nonlinear dynamic equations with delay on time scales. The obtained results generalize and improve those in related literature.