  In this paper we prove unique continuation principles for some systems of
elliptic partial differential equations satisfying a suitable superlinearity
condition. As an application, we obtain nonexistence of nontrivial (not
necessarily positive) radial solutions for the Lane-Emden system posed in a
ball, in the critical and supercritical regimes. Some of our results also apply
to general fully nonlinear operators, such as Pucci's extremal operators, being
new even for scalar equations.
