Existence Of Periodic Solutions For A Class Of Neutral Functional Differential Equations With Delay Derivatives

In this paper,we mainly discuss the existence of ω-periodic solutions,the existence and multiplicity of positive ω-periodic solutions for the second-ordered neutral functional differential equation involving x’ in f of the form(x(t)-cx(t-δ))"+a(t)g(x(t))x(t)=λb(t)f(t,x(t),x(t-τ(t)),x’(t-τ(t))),where λ is a positive parameter,c,δ are constants with |c|<1,a(t),b(t)are non-negative ω-periodic continuous functions,τi(t)(i=1,2)are continuous ω-periodic functions,f:R4→R is a continuous function and f(t,x,y,x)is ω-periodic with respect to t,g∈C(R,R).The main results of this thesis are as follows:1.Under the linear growth condition,to discuss the existence of ω-periodic so-lutions of second-ordered neutral functional differential equations with delay deriva-tives by using the Schauder’s fixed point theorem;2.Under some ordered conditions,the existence and non-existence of positiveω-periodic solutions of second-ordered neutral functional differential equations with delay derivatives is proved by using the fixed point index theory in the cone;3.By selecting a special cone,we investigate the multiplicity of positive ω-periodic solutions of second-ordered neutral functional differential equations with delay derivatives by using the positive operator perturbation method and Leggett-Williams fixed point theorem.