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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)].

MSC:
39A10 Additive difference equations
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[1] Agarwal, R.P., Difference calculus with applications to difference equations, Int. ser. num. math., 71, 95-110, (1984)
[2] Zafer, A.; Dahiya, R.S., Oscillation properties of solutions of arbitrary order neutral differential equations, (), 205-217 · Zbl 0843.34074
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