Oscillatory behaviour of a higher-order nonlinear neutral type functional difference equation with oscillating coefficients.
The authors study the oscillatory behaviour of the higher-order nonlinear difference equation of the form: \[ \Delta^n[y(k)+p(k)y(k-\tau)]+q(k)f(y(\sigma(k)))=0, \] \(n\geq 2\), \(n,k\in\mathbb{N}\); \(p(k): \mathbb N\to \mathbb{R}\) is an oscillating function; \(q(k):\mathbb{N}\to[0,+\infty)\); \(\tau\) is a positive integer, \(\sigma(k):\mathbb{N}\to\mathbb{Z}\) with \(\sigma(k)\leq k\) and \(\sigma(k)\to\infty\) as \(k\to\infty\); \(f(u)\in C(\mathbb{R},\mathbb{R})\) is a nondecreasing function, \(uf(u)>0\) for \(u\neq 0\). Two sufficient criteria are obtained.
higher-order nonlinear neutral difference equations
scientific article; zbMATH DE number 2140785