A Few Research Of Periodic Solutions Of A Kind Of Functional Points Difference Equation

Based on topological degree theory and fixed point theory, this thesis deals with the existence of periodic solutions for several kinds of functional differential equations. The thesis includes five chapters.The chapter1introduces the developing history of the functional differential equation theory meanwhile presents the structure and the main contents of this thesis. At last this part introduces some simple concepts which is related to this thesis.The chapter2discusses the existence of the positive periodic solution of the following equation x(t)=a(t)g(x(t))x(t)-λf(t, x(t-τ(t) Based on the Deimling fixed point index theorem, we get a sufficient condition for the existence of positive periodic solution, which promotes the relevant results.The chapter3discusses the existence of periodic solution of the following second-ordered neutral functional differential equations.(x(t)-cx(t-δ))=a(t)x(t)-f(t, x(t-τ(t))) Based on Kransnoselskii fixed point theorem, this chapter gets the new condition of the existence of the positive periodic solution and enriches the existing results.The chapter4discusses the existence of positive periodic solution of the following equationx(n+m+k)-a(n+m)x(n+m)-bx(n+k)+a(n)bx(n)=f(n, x(n-τ(n))) This chapter uses the function a(n) instead of the constant a, then under the fixed point theorem on core, gets the new condition of the existence of the positive periodic solution, and improves the original conclusion.The chapter5investigates the following non-autonomous discrete time predator-prey systems with delays Based on continuation theorem and invariance property of homotopy and estimation technique, this chapter gets a sufficient condition on the existence of periodic solutions for the systems.