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Generalized ordinary differential equations and discrete systems. (English) Zbl 1090.34514

The author presents some basic results of the qualitative theory of generalized ordinary differential equations introduced by J. Kurzweil [Czech. Math. J. 7, 418–449 (1957; Zbl 0090.30002)]. He also shows that this theory offers a unified approach to classical ordinary differential equations and to difference equations. As an example of this approach, some stability properties of a first order difference system are obtained as consequences of the known results of the theory of generalized differential equations. For more details of the theory of generalized differential equations see the author’s book: [Generalized ordinary differential equations (World Scientific, Singapore) (1992; Zbl 0781.34003)].

MSC:

34A99 General theory for ordinary differential equations
39A05 General theory of difference equations
26A42 Integrals of Riemann, Stieltjes and Lebesgue type
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