  We review criticality theory as a prelude to consideration of criticality of
the Grad-Shafranov equation. Novel criticality conditions of ODEs and PDEs are
derived, easily evaluated. The possibility that transport barriers are
associated with characteristics of the equilibrium equation is explored. We
conjecture that equilibrium criticality permits the appearance of new solution
branches: the high confinement branch has high poloidal flux gradient in a
diamagnetic region of the plasma. Similarly, criticality may lead to loss of
solution, which could be related to MHD instability and/or island formation
