What I wrote on the right above is not so clear. The solution
which starts with zero slope from 1 hits zero at some
finite value a which depends only on p. Scaling
this solution (by scaling x and
u simultaneously) gives all solutions which start out
with zero slope.
Above: read right board first.
Above left: unknown given map should be unknown map (erase given).
Above right: erase inner product in the middle.