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Article

Keywords:
third order difference equation; oscillation; nonoscillation; disconjugacy; generalized zero
Summary:
In this paper, sufficient conditions are obtained for oscillation of all solutions of third order difference equations of the form \[ y_{n+3} +r_{n} y_{n+2} +q_{n} y_{n+1} +p_{n} y_{n} =0,\quad n\ge 0. \] These results are generalization of the results concerning difference equations with constant coefficients \[y_{n+3} +ry_{n+2} +qy_{n+1} +py_{n} =0,\quad n\ge 0.\] Oscillation, nonoscillation and disconjugacy of a certain class of linear third order difference equations are discussed with help of a class of linear second order difference equations.
References:
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