Linearized oscillations of first-order nonlinear neutral delay difference equations

Linearized Comparison Criteria for a First Order Nonlinear Neutral Delay Difference Equation

Oscillation of second order nonlinear neutral delay difference equations

In this paper sufficient conditions are obtained for oscillation of all solutions of a class of nonlinear neutral delay difference equations of the form ∆(y(n) + p(n)y(n−m)) + q(n)G(y(n − k)) = 0 under various ranges of p(n). The nonlinear function G,G ∈ C(R,R) is either sublinear or superlinear. Mathematics Subject classification (2000): 39 A 10, 39 A 12

Necessary and sufficient conditions for oscillations of first order neutral delay difference equations with constant coefficients

In this paper, we establish the necessary and sufficient conditions for oscillation of the following first order neutral delay difference equation ∆[x(n) + px(n− τ)] + qx(n− σ) = 0, n ≥ n0, (∗) where τ and σ are positive integers, p 6= 0 is a real number and q is a positive real number. We proved that every solution of (∗) oscillates if and only if its characteristic equation (λ− 1)(1 + pλ−τ ) ...

Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...

Solvability of a Higher-Order Nonlinear Neutral Delay Difference Equation

The existence of bounded nonoscillatory solutions of a higher-order nonlinear neutral delay difference equationΔ akn · · ·Δ a2nΔ a1nΔ xn bnxn−d f n, xn−r1n , xn−r2n , . . . , xn−rsn 0, n ≥ n0, where n0 ≥ 0, d > 0, k > 0, and s > 0 are integers, {ain}n≥n0 i 1, 2, . . . , k and {bn}n≥n0 are real sequences, ⋃s j 1{rjn}n≥n0 ⊆ Z, and f : {n : n ≥ n0} × R → R is a mapping, is studied. Some sufficient...