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

Cheng Cheng | Zendy; Fushan Huang | Zendy; Yong Li | Zendy

Open Access

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

Author(s) -

Cheng Cheng,

Fushan Huang,

Yong Li

Publication year - 2016

Publication title -

journal of applied analysis and computation

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.55

H-Index - 21

eISSN - 2158-5644

pISSN - 2156-907X

DOI - 10.11948/2016062

Subject(s) - trichotomy (philosophy) , exponential dichotomy , mathematics , affine transformation , exponential function , mathematical analysis , linear differential equation , affine geometry of curves , differential equation , homogeneous , ordinary differential equation , pure mathematics , affine combination , combinatorics , philosophy , linguistics

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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