No CrossRef data available.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 24 October 2008
The theory of the exact difference equation in the general linear case has been fully developed, but the corresponding theory for the non-linear equation of the first order does not appear to have been considered. In this paper necessary and sufficient conditions for the difference equation of the first order to be exact and the form of the primitive are obtained. It appears that two conditions are required for a difference equation to be exact, one of which is identically satisfied in the limiting case of the exact differential equation. These conditions are applied to determining the primitive in some cases where the conditions for exactness are not satisfied.
* Wallenberg, Guldberg u., Theorie d. linearen Differenzengleichungen, 1911, p. 78Google Scholar. See also Nörlund, , Équations linéaires, 1929, ch. 1.Google Scholar
* See Nörlund, N. E., Acta Math. 44 (1923), 71–211.CrossRefGoogle Scholar If 
Nörlund writes,
The theory of this operator is very elaborate, but the above will serve to make the present argument intelligible.
* Nörlund, loc. cit.