Exact regions of oscillation for a difference equation with six parameters (Q1269054)

The authors tackle the difference equation \[ x_{n+1}-x_n+p x_{n-\tau}+q x_{n-\sigma}+r x_{n-\delta}=0, \quad n=0,1,\cdots \] where \(p,q,r\) are real numbers and \(\tau,\sigma,\delta\) are positive integers satisfying \(0<\tau<\sigma<\delta.\) Using the theory of envelopes as well as computer experimentation, they consider all possible values of the parameters involved in the equation and obtain a complete set of necessary and sufficient conditions for all solutions to be oscillatory.