  We prove non-uniqueness and study the behaviour of viscosity solutions of a
class of uniformly elliptic fully nonlinear equations of
Hamilton-Jacobi-Bellman-Isaacs type, with quadratic growth in the gradient. The
crucial a priori bound for the solutions is proved through an argument which
uses a boundary growth lemma, and consequences such as boundary "half"-Harnack
inequalities, which are of independent interest. Our results are new even for
linear equations.
