Annali di Matematica Pura ed Applicata

, Volume 137, Issue 1, pp 265–272 | Cite as

Periodic solutions of a class of nonlinear evolution equations

  • A. Schiaffino
  • K. Schmitt


In this paper we prove the existence of periodic solutions of abstract evolution equations which are modelled after parabolic problems. More precisely we prove that existence results follow from degree type hypotheses on the «projection» of the problem onto a suitable finite dimensional space.


Periodic Solution Evolution Equation Dimensional Space Existence Result Nonlinear Evolution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    G. Da Prato -P. Grisvard,Equations d'évolution abstraites non linéaires de type parabolique, Ann. Mat. Pura Appl.,180 (1979), pp. 329–396.Google Scholar
  2. [2]
    G. B. Gustafson -K. Schmitt,Periodic solutions of hereditary differential systems, J. Diff. Equations,13 (1973), pp. 567–587.Google Scholar
  3. [3]
    J.Hale,Oscillations in Nonlinear Systems, McGraw Hill, 1963.Google Scholar
  4. [4]
    E. Hille -R. Phillips,Functional Analysis and Semigroups, Amer. Math. Soc., Providence, 1957.Google Scholar
  5. [5]
    P. de Mottoni -A. Schiaffino,Competition systems with periodic coefficients: A geometric approach, J. Math. Biology,11 (1981), pp. 319–335.Google Scholar
  6. [6]
    N. Rouche -J. Mawhin,Ordinary Differential Equations, Stability and Periodic Solutions, Pitman, Boston, 1980.Google Scholar
  7. [7]
    A. Schiaffino,Compactness methods for a class of semilinear evolution equations, Nonl. Anal.,2 (1978), pp. 179–188.Google Scholar
  8. [8]
    J. Smoller,Shock waves and reaction-diffusion equations, Springer Verlag, New York, 1982.Google Scholar
  9. [9]
    H. B. Stewart,Generation of analytic semigroups by strongly elliptic operators under general boundary conditions, Trans. Amer. Math. Soc.,259 (1980), pp. 299–310.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1984

Authors and Affiliations

  • A. Schiaffino
    • 1
  • K. Schmitt
    • 2
  1. 1.Roma
  2. 2.Salt Lake CityUSA

Personalised recommendations