AFFINE-PERIODIC SOLUTIONS AND PSEUDO AFFINE-PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH EXPONENTIAL DICHOTOMY AND EXPONENTIAL TRICHOTOMY

Cheng Cheng; Fushan Huang; Yong Li

doi:10.11948/2016062

2016 Volume 6 Issue 4

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Cheng Cheng, Fushan Huang, Yong Li. AFFINE-PERIODIC SOLUTIONS AND PSEUDO AFFINE-PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH EXPONENTIAL DICHOTOMY AND EXPONENTIAL TRICHOTOMY[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 950-967. doi: 10.11948/2016062

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Cheng Cheng, Fushan Huang, Yong Li. AFFINE-PERIODIC SOLUTIONS AND PSEUDO AFFINE-PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH EXPONENTIAL DICHOTOMY AND EXPONENTIAL TRICHOTOMY[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 950-967. doi: 10.11948/2016062

AFFINE-PERIODIC SOLUTIONS AND PSEUDO AFFINE-PERIODIC SOLUTIONS FOR DIFFERENTIAL EQUATIONS WITH EXPONENTIAL DICHOTOMY AND EXPONENTIAL TRICHOTOMY

1 College of Mathematics, Jilin University, Changchun 130012, China;
2 School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;
3 Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, China

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Abstract

Abstract

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.
- Exponential dichotomy /
- exponential trichotomy /
- affine-periodic solutions /
- pseudo affine-periodic solutions
MSC: 34D09;34K14

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References

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