一类非自治奇异摄动系统响应解的存在性

Existence of Response Solution for A Singularly Perturbed Nonautonomous System

研究了一类拟周期奇异摄动系统拟周期解的存在性和唯一性。首先,证明了与非线性项同频率的拟周期函数可以构成一个巴拿赫空间,然后利用不动点定理和拟周期函数的B-性质,证明了该奇异摄动方程响应解,即与系统同频率的拟周期解的存在性和唯一性。

The existence and uniqueness of quasi-periodic solutions for a quasi-periodic singularly perturbed system are investigated in this paper.First,this paper shows that all quasi-periodic functions,which have the same frequency with the nonlinear terms,form a Banach space.Then the the existence and uniqueness of response solution are obtained for the above singularly perturbed system by means of the fixed point methods and the B-property of quasi-periodic functions.