Oscillation criteria for certain difference equations with continuous vairables

This paper is concerned with the delay difference equation x (t) - x (t - r) + Sigma(m)(i=1) p(i) (t) x (t- sigma(i)) = 0, t >= 0, where 0 < tau < sigma 1 < ... < sigma(m), pi is an element of C (R, R+), lim inf(t ->infinity) pi (t)= (p) over bari >= 0, i = 1, 2, ... m. We establish some new sufficient conditions for the oscillation of all solutions of the above equation x(t) - x(t -tau) + Sigma(m)(i=1) (p) over bar (i)x(t - sigma(i)) = 0, t >= 0 admits non-oscillatory solutions and improve the previous corresponding results about the above equation (see [1,3-7]).