  Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv)
is an interesting computational challenge, outside the reach of the
well-developed methods for nonlinear eigenvalue problems. We present a natural
generalization of these methods which leads to a contour integration approach
for computing all eigenvalues of a PEPv in a compact region of the complex
plane. Our methods can be used to solve any suitably generic system of
polynomial or rational function equations.
