具有周期扰动的差分方程的周期解

On the Periodic Solution for the Difference Euqations with Periodic Disturbance

考虑了一类扰动的差分方程:x(n+1)-x(n)=b(n,xn)+f(n,xn).利用广义度理论证明了方程在对应齐次线性方程只有平凡的N周期解的情况下至少存在一个N周期解.应用此结果,得到了周期解的存在唯一性准则.

In this paper is concerned with a closs of difference equation with disturbance： x（n＋1）-x（n）=b（n,xn）＋f（n,xn） It proves by the generalized degree theory that the equation has at least one N - periodic solution if the corresponding homoge- neous euqation has only a triveal N - periodic solution. By this result, the criteria of existence and uniqueness of the periodic solution is obtained.