Oscillation criterion for generalized Euler difference equations

Using a modification of the adapted Riccati transformation, weprove an oscillation criterion for generalizations of linear and half-linear Euler differenceequations. Our main result complements a large number of previouslyknown oscillation criteria about several similar generalizations of Euler differenceequations. The major part of this paper is formed by the proof of the main theorem.To illustrate the fact that the presented criterion is new even for linearequations with periodic coefficients, we finish this paper with the correspondingcorollary together with concrete examples of simple equations whose oscillatoryproperties do not follow from previously known criteria.