Exponential Dichotomies and Fredholm Operators of Dynamic Equations on Time Scales
| Autor: | Le Huy Tien, Le Duc Nhien |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Fredholm operator Exponential dichotomy 010102 general mathematics Linear system Scale (descriptive set theory) General Medicine 01 natural sciences Exponential function 010101 applied mathematics Operator (computer programming) Bounded function 0101 mathematics Associative property Mathematics |
| Zdroj: | Applied Mathematics. 10:39-50 |
| ISSN: | 2152-7393 2152-7385 |
| DOI: | 10.4236/am.2019.101004 |
| Popis: | For time-varying non-regressive linear dynamic equations on a time scale with bounded graininess, we introduce the concept of the associative operator with linear systems on time scales. The purpose of this research is the characterizations of the exponential dichotomy obtained in terms of Fredholm property of that associative operator. Particularly, we use Perron’s method, which was generalized on time scales by J. Zhang, M. Fan, H. Zhu in [1], to show that if the associative operator is semi-Fredholm then the corresponding linear nonautonomous equation has an exponential dichotomy on both T + and T-. Moreover, we also give the converse result that the linear systems have an exponential dichotomy on both T + andT- then the associative operator is Fredholm on T. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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