Multiple solutions for nonlinear functional difference equations by the invariant sets of descending flow.

In this paper, by employing the invariant sets of descending flow in combination with variational methods, we establish some new criteria to ensure that a class of second-order nonlinear difference equations containing both advance and retardation with different boundary conditions admit at least four distinct solutions which are composed of sign-changing solutions, positive solutions, negative solutions and trivial solution. Furthermore, as an application of our theoretical results, two examples are presented. [ABSTRACT FROM AUTHOR]