It is shown that simple functional dependencies of transport coefficients on plasma parameters can result in a transition in the particle and energy confinement near the edge of a tokamak where particle sources, and hence convection, are important. This is illustrated using cylindrical classical diffusion coefficients. The transition may be to a second steady state or to a regime where there is no steady solution, in which the density rises continuously, for instance. In practice such a density rise would be curtailed by high radiated power or by instabilities. Many experimental obserllations of L to H-mode transitions in tokamaks coincide with the non-steady solution rather than a bifurcation to a second steady state.