Multiplicity results for nonlinear periodic fourth order difference equations with parameter dependence and singularities

This paper is devoted to the study of nonlinear singular and non-singular fourth order difference equations coupled with periodic boundary value conditions. In the paper some existence and nonexistence results are given. The results are deduced from Krasnoselskiiʹs fixed point theorems in cones. An exhaustive study of the Greenʹs function related to a linear fourth order problem is done.