  We study the inverse problem of determining uniquely and stably quasilinear
terms appearing in an elliptic equation from boundary excitations and
measurements associated with the solutions of the corresponding equation. More
precisely, we consider the determination of quasilinear terms depending
simultaneously on the solution and the gradient of the solution of the elliptic
equation from measurements of the flux restricted to some fixed and finite
number of points located at the boundary of the domain generated by Dirichlet
data lying on a finite dimensional space. Our Dirichlet data will be explicitly
given by affine functions taking values in $\mathbb R$. We prove our results by
considering a new approach based on explicit asymptotic properties of solutions
of these class of nonlinear elliptic equations with respect to a small
parameter imposed at the boundary of the domain.
