Oscillation of Second Order Difference Equation with a Sub-linear Neutral Term

Oscillation for a second-order neutral differential equation with impulses

We consider a certain type of second-order neutral delay differential systems and we establish two results concerning the oscillation of solutions after the system undergoes controlled abrupt perturbations (called impulses). As a matter of fact, some particular non-impulsive cases of the system are oscillatory already. Thus, we are interested in finding adequate impulse controls under which our...

Oscillation of Second Order Neutral Difference Inequalities with Oscillating Coefficients

In this paper, we established some sufficient conditions for the oscillation of second order neutral difference inequalities (−1)x(n) { ∆z(n) + (−1)q(n)f(x(σ(n))) } ≤ 0, n ≥ n0 (∗) where δ = 0 or δ = 1, z(n) = x(n) + p(n)x(n − τ), τ is a positive integer, {p(n)}, {q(n)} are sequences of real numbers, {σ(n)} is a sequence of nonnegative integers and f : R → R where R is the set of real numbers. ...

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...

Oscillation Criteria of Solution for a Second Order Difference Equation with Forced Term

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