OSCILLATIONS OF DIFFERENCE-EQUATIONS WITH POSITIVE AND NEGATIVE COEFFICIENTS

We obtain sufficient conditions for the oscillation of all solutions of some difference equations with positive and negative coefficients. Our results include the following: Consider the difference equation (1) An+1 - An + pAn-k - qAn-1 = 0, n = 0, 1, 2,..., where p and q are nonnegative real numbers and k and l are nonnegative integers such that p > q greater-than-or-equal-to 0, k greater-than-or-equal-to l greater-than-or-equal-to 0, q(k-1) less-than-or-equal-to 1 and [GRAPHICS] Then every solution of Equation (1) oscillates. Extensions to equations with variable coefficients were also obtained.