Geodesic
Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order
Mathematica Bohemica, Tome 133 (2008) no. 1, pp. 99-112

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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.
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.
DOI : 10.21136/MB.2008.133942
Classification : 39A06, 39A10, 39A11, 39A12, 39A21
Keywords: third order difference equation; oscillation; nonoscillation; disconjugacy; generalized zero 
Parhi, N.; Panda, Anita. Oscillatory and nonoscillatory behaviour of solutions of difference equations of the third order. Mathematica Bohemica, Tome 133 (2008) no. 1, pp. 99-112. doi: 10.21136/MB.2008.133942
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