科研之友
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摘要
It is proved that every (Q, T)-affine-periodic differential equation has a (Q, T)-affine-periodic solution if the corresponding homogeneous linear equation admits exponential dichotomy or exponential trichotomy. This kind of "periodic" solutions might be usual periodic or quasi-periodic ones if Q is an identity matrix or orthogonal matrix. Hence solutions also possess certain symmetry in geometry. The result is also extended to the case of pseudo affine-periodic solutions.
