  In \cite{LWZ}, we establish Liouville-type theorems and decay estimates for
solutions of a class of high order elliptic equations and systems without the
boundedness assumptions on the solutions. In this paper, we continue our work
in \cite{LWZ} to investigate the role of boundedness assumption in proving
Liouville-type theorems for fully nonlinear equations. We remove the
boundedness assumption of solutions which was required in the proof of
Liouville-type theorems for fully nonlinear elliptic equations or systems in
half spaces. We also prove the Liouville-type theorems for supersolutions of a
system of fully nonlinear equations with Pucci extremal operators in half
spaces.
