Some new results for bounded and monotone properties of solutions of second-order quasi-linear forced difference equations

Some new results are obtained for the bounded and monotone properties of solutions of second-order quasi-linear forced difference equations δ(Pn−1(δYn−1)α)=qnYnβ+rn, n≥n0, where n0 ε N = {0,1,2,3,…}, {pn}n=n0−1∞ is a positive sequence, {qn}n=n0∞ is a nonnegative real sequence with qn 0, {rn}n=n0∞ is a real sequence, and α and β are quotients of odd positive integers. Some errors in [1] are pointed out and addressed. Examples are given to illustrate the advantages of the new results.