Existence of a nonoscillatory solution of a second-order linear neutral difference equation

Consider the neutral delay difference equation with positive and negative coefficients, Δ2(xn+pxn−m)+pnxn−k−qnxn−l=0, where p∈Rp∈R and m,k,l∈Nm,k,l∈N and pn,qn∈R+,n≥n0∈Npn,qn∈R+,n≥n0∈N.Some sufficient conditions for the existence of a nonoscillatory solution of the above equation expressed in terms of ∑∞ipi<∞,∑∞iqi<∞∑∞ipi<∞,∑∞iqi<∞ are obtained.