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Volume 6, Number 4, 2016, Pages 950-967                                                                DOI:10.11948/2016062
Affine-Periodic Solutions and Pseudo Affine-Periodic Solutions for Differential Equations with Exponential Dichotomy and Exponential Trichotomy
Cheng Cheng,Fushan Huang,Yong Li
Keywords:Exponential dichotomy, exponential trichotomy, affine-periodic solutions, pseudo affine-periodic solutions.
      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.
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