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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)].

39A10 Additive difference equations
Full Text: DOI
[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
[3] Zafer, A.; Dahiya, R.S., Oscillatory asymptotic behavior of solutions of third order delay differential equations with forcing terms, Dif. equations and dyn. systems, 1, 123-136, (1993) · Zbl 0872.34045
[4] Agarwal, R.P., Properties of solutions of higher order nonlinear difference equations II, (), 85-96, Al. I Cuza, lasi
[5] Agarwal, R.P., Difference equations and inequalities, (1992), Marcel Dekker New York · Zbl 0784.33008
[6] Bihari, I., A generalization of a lemma of Bellman and its applications to uniqueness problems of differential equations, Acta. math. acad. sci. hungar., 7, 81-94, (1957) · Zbl 0070.08201
[7] Cheng, S.S.; Yan, T.C.; Li, H.J., Oscillation criteria for second order difference equation, Funkcialaj ekvacioj, 34, 223-239, (1991) · Zbl 0773.39001
[8] Grammatikopoulos, M.K.; Grove, E.A., Oscillation and asymptotic behavior of neutral differential equations with deviating arguments, Applicable anal., 22, 1-19, (1986) · Zbl 0566.34057
[9] Zhicheng, W.; Jianshe, Y., Oscillation of second order nonlinear difference equations, Funkcialaj ekvacioj, 34, 313-319, (1991) · Zbl 0742.39003
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