Oscillation and non-oscillation of solutions of second order difference equations involving generalized difference

Abstract

In this paper, sufficient conditions are obtained for oscillation/non-oscillation of solutions of second order difference equations, involving generalized difference, of the form. △a(p(n-1)△a y(n-1))+q(n)y(n)=0, n≥1 and △a(p(n-1)△a y(n-1))+q(n)y(n)=f(n), n≥1 where △a is defined by △a y(n)=y(n +1) - ay(n), a≠ 0. Necessary and sufficient conditions are obtained for oscillation of the first equation with a > 0 and q(n)=q, a non-zero constant. The signs of q(n) and a play an important role for oscillation/non-oscillation of these two equations.