On unique continuation principles for some elliptic systems

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