一类四阶差分方程的多重周期解

In this paper, we consider the multiplicity of periodic solutionsfor a class of fourth-order difference equations. We establish some sufficientconditions on the multiplicity of periodic solutions for the fourth-order difference equations egin{eqnarray*}Delta^{2}(r_{n-2}Delta^{2}x_{n-2})+f(n,x_{n})=0, ninmathbb{Z},end{eqnarray*}where $Delta$ is the forwarddifference operator $Delta x_{n}=x_{n+1}-x_{n},Delta^{2}x_{n}=Delta(Delta x_{n})$. Byestablishing a proper variational set, two multiplicity results areobtained by means of somemultiple critical points theorems.