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Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order. (English) Zbl 1199.39016
Summary: Sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form \[ y_{n+3} +r_{n} y_{n+2} +q_{n} y_{n+1} +p_{n} y_{n} =0,\quad n\geq 0. \] These results are generalization of the results concerning difference equations with constant coefficients \[ y_{n+3} +ry_{n+2} +qy_{n+1} +py_{n} =0,\quad n\geq 0. \] Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with the help of a class of linear second order difference equations.

MSC:
39A21 Oscillation theory for difference equations
39A06 Linear difference equations
39A10 Additive difference equations
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