Bounded and monotone properties of solutions of second-order quasilinear forced difference equations

The authors consider the quasilinear difference equation δ(pn−1(δyn−1)α)=qnyβn+rn and obtain results on the asymptotic behavior of solutions of (*) including sufficient conditions for all solutions to be bounded or unbounded. Some results on the existence and behavior of nonincreasing solutions of (*) are also obtained. Examples are inserted to illustrate the results.