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Summary

In this paper first and second order linear delay differential operators in periodic function spaces are considered. Some conditions in order that these operators are of “monotonie type”, that is isotonic if Lu≤lv implies u≤v and antitonic if Lu≤lv implies u≥v, are given. It is considered the case of a variable delay τ=τ(t) and, separately, that of a constant delay τ. The first one is more general, as well as the conditions which are found. On the contrary, for constant delays, optimal results are obtained.

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References

  1. [1]
    A. Bellen: Cohen’s iteration process for boundary value problems for functional differential equations. Rend.Ist.Mat.Univ. Trieste 11,32–46(1979).Google Scholar
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    L. Collatz: The numerical treatment of differential equations. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960.CrossRefGoogle Scholar
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    M. Zennaro: A class of linear operators in periodic function spaces including difference-differential operators. To appear.Google Scholar
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    M. Zennaro: Maximum principles for linear difference-differential operators in periodic function spaces. To appear.Google Scholar

Copyright information

© Springer Basel AG 1983

Authors and Affiliations

  • A. Bellen
    • 1
  • M. Zennaro
    • 1
  1. 1.Istituto di MatematicaUniversità degli StudiTriesteItaly

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