Inverse problems for semilinear elliptic PDE with measurements at a single point

We consider the inverse problem of determining a potential in semilinear elliptic equation from knowledge Dirichlet-to-Neumann map. For bounded Euclidean domains we prove that is uniquely determined by map measured at single boundary point, or integrated against fixed measure. This result valid even when Dirichlet data only given on small subset boundary. also give related uniqueness results Riemannian manifolds.