please help me in solving this problem with a discrete non linear set of equations.

x is a vector of discrete values (+1,-1)
phi is a non linear function defined in R and taking all the values in [-1,1] as a monotonic increasing function
sgn is a sign function so that sgn(x) = +1 if x if x>=0 and -1 otherwise

A and B are two matrices of real numbers.

I have to find the vector x that satisfies the relation
x = sgn(B*phi(A*x))

i don't' know if there exists a solution for this kind of equations set, please help me and if possible explain me why a solution can exists and how I could find it.

Thanx very much