ABSTRACT. The second order difference equation (E) A2xn+p"f(xn) = 0 is considered. The results give a necessary and sufficient condition for some solution of (E) to have asymptotic behavior x" ~ C = const, as n approaches infinity.Introduction. The asymptotic behavior of the solutions of second order differential equations have been considered by R. A. Moore and Z. Nehari [4], W. F. Trench [9], and P. Waltman [10]. The next results for nth order nonhomogeneous differential equations was given by T. G. Hallam [1,2]. Similar problems with regard to second order difference equations were investigated by J.

For some class of the finite difference equations oscillation criteria are given.Let R be the set of all real numbers. We let N(nQ) = = |nQ,n0+1,...}, where nQ is a natural number or zero. Let a > 0 be a real constant. The difference operator A^ will be defined in the following way AQ*n = xQ+1 -axQ (neN(O)), where jxQj is the sequence of real numbers. Instead of A^ we shall write A.In this paper we study oscillation

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