Oscillation of second-order nonlinear difference equations with sublinear neutral term

Abstract

We establish some new criteria for the oscillation of secondorder nonlinear difference equations with a sublinear neutral term. This is accomplished by reducing the involved nonlinear equation to a linear inequality.

Oscillation of second order nonlinear difference equations with super-linear neutral term

“…The obtained results simplifies the known results in the literature in the sense that we need only one condition instead of two conditions required in [7,9,11] for the oscillation of all solutions of equation (1.1). Further the results presented in this paper extend and generalize the results known [4][5][6][15][16][17][18] for the case 0 < α < 1 to the case α > 1.…”

“…First we give an example for the case β > 1. Here α > 1 is a quotient of odd integers, β = 3, the delays k ≥ 1 and ≥ 0, and a n = n(n+1), p n = 1 n 2 and q n = (n+1) 5 . We set γ = 1.…”

Oscillatory behavior of second order delay dynamic equations with a sub-linear neutral term on time scales

“…However, it seems that there are no known results for the oscillation of second-order dynamic equations with positive sublinear neutral terms. Also, in special cases T = R and T = Z there are a few literature present sufficient criteria for the oscillatory behavior of second-order differential equations and difference equations with positive sublinear neutral terms, see; [1,4,6,[12][13][14][15][16]25].…”