MATHEMATICA BOHEMICA, Vol. 133, No. 1, pp. 99-112 (2008)

Oscillatory and nonoscillatory behaviour of
solutions of difference equations of
the third order

N. Parhi, Anita Panda

N. Parhi MIG-II, No. 249, Satya Sai Enclave, Khandagiri, Bhubaneswar 751030, India, e-mail:; Anita Panda, IcfaiTech, Bhubaneswar, A-123, Mancheswar Industrial Estate-751010, India, e-mail: anitapanda\

Abstract: 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\ge0.
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\ge0.
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.

Keywords: third order difference equation, oscillation, nonoscillation, disconjugacy, generalized zero

Classification (MSC2000): 39A10, 39A12

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