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{ K1.1/ ? K1.1 ilk=MATRIX K2.1/ K2.2/ K2.3/ /K1.1 K2.1 ilk=MATRIX x(t+2k)-∑_{i=0}^{2k-1}a_{i}x(t+i)=f(t,x(t),x(t+1),...,x(t+2k-1)),t in [0,T-1], /K2.1 K2.2 ilk=MATRIX x(i)=A_{i},i in [0,k-1], /K2.2 K2.3 ilk=MATRIX x(T+2k-1-i)=B_{i},i in [0,k-1] /K2.3 at non-resonance case are established. Examples are given to show the efficiency of the result in this paper.