Georgian Mathematical Journal

, Volume 2, Issue 1, pp 1–8 | Cite as

Continuous transformations of differential equations with delays

  • Jan Čermák
Article

Abstract

The aim of this paper is to find the class of continuous pointwise transformations (as general as possible) in the framework of which Kummer's transformationz(t)=g(t)y(h(t)) represents the most general pointwise transformation converting every linear homogeneous differential equation of thenth order into an equation of the same type. Further, some forms of these equations having certain subspaces of solutions are considered.

1991 Mathematics Subject Classification

34K05 34K15 

Key words and phrases

Differential equation delay argument transformation 

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References

  1. 1.
    P. Stäckel, Über Transformationen von Differentialgleichungen.J. Reine Angew. Math. 111 (1893), 290–302.Google Scholar
  2. 2.
    M. Čadek, Form of general pointwise transformations of linear differential equations.Czechoslovak Math. J. 35(110) (1985), 617–624.Google Scholar
  3. 3.
    F. Neuman, Global Properties of Linear Differential Equations.Academic, Prague, 1991.Google Scholar
  4. 4.
    V. Tryhuk, The most general transformation of homogeneous retarded linear differential equations of thenth order.Math. Slovaka 33 (1983), 15–21.Google Scholar
  5. 6.
    J. K. Hale, Functional Differential Equations,Springer-Verlag, New York, 1971.Google Scholar
  6. 5.
    F. Neuman, Geometrical approach to linear differential equations of thenth order.Rend. Mat. 5 (1972), 572–602.Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • Jan Čermák
    • 1
  1. 1.Department of MathematicsTechnical University of BrnoBrnoCzech Republic

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