Classification of nonoscillatory solutions of second order self-adjoint neutral difference equations (Q1429002)

Classification schemes for eventually positive solutions of a class of neutral difference equation of the form \[ \Delta \left( a_n\left| \Delta \left( x_n-p_nx_{\tau _n}\right) \right| ^\alpha \text{sgn}\Delta \left( x_n-p_nx_{\tau _n}\right) \right) +f\left( n,x_{g_n}\right) =0 \] are given in terms of their asymptotic magnitudes, and sufficient conditions for the existence of these solutions are also provided.