New criteria for the oscillation and existence of monotone solutions of second-order nonlinear difference equations

摘要

We obtain sufficient conditions for the oscillation of the perturbed difference equation Delta(a(n-1)(Delta gamma(n-1))(sigma)) + F(n,gamma(n)) = G(n,gamma(n), Delta gamma(n)), n greater than or equal to 1 as well as for the existence of monotone solutions of the nonlinear difference equation Delta(a(n-1)(Delta gamma(n-1))(sigma))+k(n)f(gamma(p(n))) = 0, n greater than or equal to 1, where 0 < sigma = p/q with p even and q odd integers, and some incorrect results in a recent paper are pointed out. Examples which illustrate the importance of our results are also included. (C) 2000 Elsevier Science Inc. All rights reserved. [References: 18]