Non-oscillatory solutions of higher order nonlinear neutral delay difference equations
The author considers the higher order neutral difference equation \[ L_m(x(n) + cx(n-\tau)) + F(n, x(\sigma(n))) = g(n), n \geq n_0, \tag{1} \] where \(L_0 x(n) = x(n)\), \(L_i x(n) = \Delta (L_{i-1} x(n))/r_i(n)\), \(i =1,\dots, m\), \(\Delta x(n) = x(n+1) - x(n)\), \(c\) is a real parameter. It is assumed that \(r_i > 0\), \(i=1,\dots,m-1,\) and \(r_m \equiv 1.\) Sufficient conditions for the existence of a bounded non-oscillatory solution of (1) are obtained.
higher order neutral difference equation
scientific article; zbMATH DE number 2075239