Integral Equations and Operator Theory

, Volume 32, Issue 3, pp 332–353 | Cite as

Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line

  • Nguyen Van Minh
  • Frank Räbiger
  • Roland Schnaubelt
Article
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Abstract

LetU=(U(t, s)) t≥s≥O be an evolution family on the half-line of bounded linear operators on a Banach spaceX. We introduce operatorsGO,G X andI X on certain spaces ofX-valued continuous functions connected with the integral equation\(u(t) = U(t,s)u(s) + \int_s^t {U(t,\xi )f(\xi )d\xi }\), and we characterize exponential stability, exponential expansiveness and exponential dichotomy ofU by properties ofGO,G X andI X , respectively. This extends related results known for finite dimensional spaces and for evolution families on the whole line, respectively.

1991 Mathematics Subject Classification

Primary 34G10 47D06 Secondary 47H20 
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Copyright information

© Birkhäuser Verlag 1998

Authors and Affiliations

  • Nguyen Van Minh
    • 1
  • Frank Räbiger
    • 2
  • Roland Schnaubelt
    • 2
  1. 1.Department of MathematicsUniversity of HanoiHanoiVietnam
  2. 2.Mathematisches InstitutUniversität TübingenTübingenGermany

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