Oscillations and nonoscillations of half-linear difference equations generated by deviating arguments. (English) Zbl 0933.39025

Wong, P. J. Y.; Agarwal, R. P.

Comput. Math. Appl. 36, No. 10-12, 11-26 (1998).

Summary: For the half-linear difference equation \[ \Delta\biggl[ \bigl|\Delta y(k) \bigr|^{\alpha-1} \Delta y(k)\biggr]= \sum^n_{i=1} p_i(k)\biggl |y\bigl( g_i(k)\bigr) \biggr|^{\alpha-1}y \bigl(g_i (k) \bigr),\;k\geq a, \] where \(\alpha>0\), we shall offer sufficient conditions for the oscillation of all solutions, as well as necessary and sufficient conditions for the existence of both bounded and unbounded nonoscillatory solutions. Several examples which dwell upon the importance of our results are also included.

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

deviating arguments; half-linear difference equation; oscillation; bounded and unbounded nonoscillatory solutions

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