Existence of Solutions of BVPs for Nonlinear Difference Equations: Non-resonance Case

Sufficient conditions for the existence of solutions of the following boundary value problem for nonlinear difference equation{┊x(t+2k)-∑_{i=0}^{2k-1}a_{i}x(t+i)=f(t,x(t),x(t+1), ,x(t+2k-1)),t∈[0,T-1],x(i)=A_{i},i∈[0,k-1],x(T+2k-1-i)=B_{i},i∈[0,k-1]at non-resonance case are established. Examples are given to show the efficiency of the result in this paper.