  In this paper we characterize the degenerate elliptic equations F(D^2u)=0
whose viscosity subsolutions, (F(D^2u) \geq 0), satisfy the strong maximum
principle. We introduce an easily computed function f(t) for t > 0, determined
by F, and we show that the strong maximum principle holds depending on whether
the integral \int dy / f(y) near 0 is infinite or finite. This complements our
previous work characterizing when the (ordinary) maximum principle holds. Along
the way we characterize radial subsolutions.
