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

摘要

In this paper, sufficient conditions are obtained for oscillation/non-oscillation of solutions of second order difference equations, involving generalized difference, of the form.Δa(p(n-1)Δay(n-1))+q(n)y(n)=0,n⩾1andΔa(p(n-1)Δay(n-1))+q(n)y(n)=f(n),n⩾1,where Δa is defined by Δay(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.