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Oscillation theory of linear difference equations. (English) Zbl 1090.39001

The author presents the survey of the basic results of linear discrete oscillation theory. In particular, there is given the central statement of the oscillation theory of Sturm-Liouville linear difference equation, namely the so-called Roundabout theorem, which provides powerful tools for the investigating of oscillatory properties. As an application of these methods the author proves oscillation and nonoscillation criteria. Further, there are presented two theorems concerning trigonometric and Prüfer transformation of certain symplectic difference system. The last part of the paper is devoted to the higher order linear difference equation, where it is shown Pólya factorization and oscillation criterion for this equation.

MSC:

39A10 Additive difference equations
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