Frequent Oscillation Criteria for a Delay Difference Equation

Oscillation Criteria for Delay Equations

This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form x′(t) + p(t)x(τ(t)) = 0, t ≥ t0, (1) where p, τ ∈ C([t0,∞),R),R = [0,∞), τ(t) is non-decreasing, τ(t) < t for t ≥ t0 and limt→∞ τ(t) =∞. Let the numbers k and L be defined by

Oscillation Criteria for Hamiltonian Matrix Difference Systems

We obtain some oscillation criteria for the Hamiltonian difference system (AY{t) = B{t)Y{t+\) + C{t)Z{t), I AZ{t) = -A{t)Y{t + 1) B*{t)Z{t), where A, B, C, Y, Z are dxd matrix functions. As a corollary, we establish the validity of an earlier conjecture for a second-order matrix difference system.

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

On a Difference-delay Equation

We investigate how the behaviour, especially at 1; of continuous real solutions f (t) to the equation f (t) = a 1 f (t + h 1) + a 2 f (t ? h 2); where a 1 ; a 2 ; h 1 ; h 2 are positive real constants, depends on the values of these parameters. Deenitive answers are given, except in certain cases when h 1 =h 2 is rational..