Response Solutions for a Singularly Perturbed System Involving Reflection of the Argument

In this paper, the existence and uniqueness of response solutions, which has the same frequencyωwith the nonlinear terms, are investigated for a quasiperiodic singularly perturbed system involving reflection of the argument. Firstly, we prove that all quasiperiodic functions with the frequencyωform a Banach space. Then, we obtain the existence and uniqueness of quasiperiodic solutions by means of the fixed-point methods and theB-property of quasiperiodic functions.