Exponential Dichotomies: Continuous Time

  • Luís Barreira
  • Davor Dragičević
  • Claudia Valls
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


This chapter is dedicated to the study of the admissibility theory for exponential dichotomies in continuous time. Again, the arguments build on those in Chapter  2, up to substantial technical complications. To the possible extent, we follow the path of Chapter  3. In particular, we consider both a two-sided and a one-sided dynamics given by an evolution family.


  1. 8.
    L. Barreira, C. Valls, Admissibility in the strong and weak senses, Preprint IST, 2017Google Scholar
  2. 10.
    L. Barreira, D. Dragičević, C. Valls, Strong and weak (L p, L q)-admissibility. Bull. Sci. Math. 138, 721–741 (2014)MathSciNetCrossRefGoogle Scholar
  3. 14.
    L. Barreira, D. Dragičević, C. Valls, Admissibility on the half line for evolution families. J. Anal. Math. 132, 157–176 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 23.
    W. Coppel, Dichotomies in Stability Theory. Lecture Notes in Mathematics, vol. 629 (Springer, New York, 1981)Google Scholar
  5. 33.
    D. Henry, Exponential dichotomies, the shadowing lemma and homoclinic orbits in Banach spaces. Resenhas 1, 381–401 (1994)MathSciNetzbMATHGoogle Scholar
  6. 38.
    Y. Latushkin, T. Randolph, R. Schnaubelt, Exponential dichotomy and mild solutions of nonautonomous equations in Banach spaces. J. Dyn. Differ. Equ. 10, 489–510 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 72.
    A. Sasu, Exponential dichotomy for evolution families on the real line. Abstr. Appl. Anal. 2006, 31641, 16 pp. (2006)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Luís Barreira
    • 1
  • Davor Dragičević
    • 2
  • Claudia Valls
    • 1
  1. 1.Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal
  2. 2.Department of MathematicsUniversity of RijekaRijekaCroatia

Personalised recommendations