Weakly nonlinear discrete multipoint boundary value problems

In this paper we study nonlinear, discrete, multipoint boundary value problems of the formx(t+1)=A(t)x(t)+ϵf(t,x(t))x(t+1)=A(t)x(t)+ϵf(t,x(t)) subject toB0x(0)+B1x(1)+⋯+BNx(N)=0.B0x(0)+B1x(1)+⋯+BNx(N)=0.We provide sufficient conditions for the existence of solutions and we present a qualitative analysis of the way the solutions depend on the parameter ϵ.