时标上的二阶中立型泛函微分方程的周期解

PERIODIC SOLUTION OF SECOND-ORDER NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS ON TIME SCALES

利用叠合度理论研究了一类时标上的二阶中立型泛函微分方程,得到方程(x(t)-c(t)x(t-T))△△=-a(t)f(x(t))△(t)-Σ i=1nbi(t)gi(t,x(t-Ti(t)))周期解存在的条件,其中a,bi和,TiC(T,R)都是w-周期函数T是常时滞且T﹥0, c (t )C2(T,R), 0 ≤c(t)〈1, g iC(T* R, R +), i =1,2, ...,,n关于第一个分量是w-周期函数,关于第二个分量是非减的,c(t)C2(T,R)。

We consider one type of second-order neutral functional differential equations on time scales. By applying the continuation theorem of coincidence degree theory, we establish the existence of periodic solutions to the equation （x（t）-c（t）x（t-τ））？？=-a（t）f（x（t））x？（t）-nΣi=1bi（t）gi（t,x（t-τi（t））） where a,bi and τi∈C（T,R）are ω-periodic functions,τis a constant delay and τ〉0,0≤c（t）〈1,gi∈C（T×R,R＋）,I=1,2,...,n are non-decreasing with respect to their second arguments andω-periodic with respect to their first arguments, respectively.