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Oscillatory and asymptotic behavior of higher order difference equations. (English) Zbl 0820.39001
The author obtains sufficient conditions for the oscillation of all bounded solutions of the neutral difference equation $\Delta(a(t) \Delta^{n- 1} (x(t)+ p(t) x(\eta(t))))+ F(t, x(\sigma(t)))= 0,\quad t\in I$ and the asymptotic behavior of solutions of the delay difference equation $\Delta^ n x(t)+ F(t, x(g(t)))= h(t),\quad t\in I.$ For related works see R. P. Agarwal [An. Sţiint. Univ. Al. I. Cuza Iaşi, N. Ser., Sect. Ia 29, No. 3, Suppl., 85-96 (1983; Zbl 0599.39002)].