The Qualitative Property For Some Types Of Functional Differential Equations

In this paper, we discuss the qualitative property for some types of functionaldifferential equations.This paper includes three main parts as follows. In Chapter2, by usingdifferential inequalityand Lyapunov function,we discuss the predator-prey model withModified Leslie-Gower Holling-typeII schemes. Sufficient conditions are obtainedwhich guarantee the uniform persistence and gl-obal attractivity of positive solutionfor the model. Then some criteria are established for the exist-ence, uniqueness andglobal attractivity of positive almost periodic solution of almost periodic sy-stem. InChapter3, by using differential inequality and Lyapunov function, we study thepredator-prey model with delay and Modified Leslie-Gower Holling-typeII schemes.Sufficient conditions are obtained which guarantee the uniform persistence and globalattractivity of positive solution f-or the model. Then some criteria are established forthe existence, uniqueness and global attractiv-ity of positive almost periodic solutionof almost periodic system. In Chapter4, by using a genera-lization of theLeggett-Williams fixed-point theorem due to Avery and Peterson, we discuss theb-oundary problem with delay and one-dimensional p-Laplacian. Sufficientconditions are obtained which guarantee the existence of at least three positivesolutions.