In a previous paper, I developed the analogues for incompressible, finite, elasticity to results obtained by Ball and Marsden, and by Simpson and Spector for the compressible case. Specifically, a condition of quasiconvexity at the boundary, its weak version-the localized second variation condition, and conditions necessary and sufficient for the truth of the latter were found. Here, in emulation of results of Mielke and Sprenger for compressible elasticity, I recast the aforementioned necessary and sufficient conditions in an equivalent, variational form. In nonsingular cases, Agmon's condition is shown to be equivalent to the condition that a certain algebraic Riccati equation should possess a positive-semidefinite solution. The implications of this condition are explored for various special situations.