Bulletin of the
Korean Mathematical Society BKMS

Using Minimax principle and Linking theorem in critical point theory, we prove the existence of two nontrivial solutions for the following second order superlinear difference systems \[ (P)\left \{ \begin{array}{ll} \Delta^{2}x(k-1)+g(k,y(k))=0,&{k\in [1,T],}\\ \Delta^{2}y(k-1)+f(k,x(k))=0,&{k\in [1,T],}\\ x(0)=y(0)=0,x(T+1)=y(T+1)=0, \end{array} \right. \] where $T$ is a positive integer, [1,T] is the discrete interval $\{1,2,\ldots,$ $T\}, \Delta x(k)=x(k+1)-x(k)$ is the forward difference operator and $\triangle^{2}x(k)=\triangle(\triangle x(k))$.

Keywords: difference systems, multiple, critical point theory, super-linear

MSC numbers: 34B16, 39A10