Existence and nonexistence results on the radially symmetric cavitation problem

We investigate the problem of radially symmetric cavitation for a hyperelastic ball in $\mathbb {R}{^n} , n \ge 2$. The radial equilibrium equation is analyzed by a shooting argument. The basic formulation of the problem is the same as C. A. Stuart’s formulation in [10], but an asymptotic study of the solutions of the radial equilibrium equation allows us to enlarge the discussion of cavitation to cases that are excluded from the context of [10]. Finally, criteria for nonexistence to the problem of cavitation are briefly discussed. They have a physical interpretation through relations between the total energy and the radial stress.