Comparison and linearized oscillation theorems for a nonlinear partial difference equation

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...

Linearized Oscillation of Nonlinear Difference Equations with Advanced Arguments

This paper is concerned with the nonlinear advanced difference equation with constant coefficients

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

Oscillation theorems for second-order nonlinear delay difference equations

By means of Riccati transformation technique, we establish some new oscillation criteria for second-order nonlinear delay difference equation ∆(pn (∆xn) ) + qnf(xn−σ) = 0, n = 0, 1, 2, . . . ,

Linearized oscillation theory for a nonlinear equation with a distributed delay

We obtain linearized oscillation theorems for the equation with distributed delays ẋ(t)+ m ∑ k=1 rk(t) ∫ t −∞ fk(x(s)) ds Rk(t, s) = 0. (1) The results are applied to logistic, Lasota–Wazewska and Nicholson’s blowflies equations with a distributed delay. In addition, the “Mean Value Theorem” is proved which claims that a solution of (1) also satisfies the linear equation with a variable concent...