  In the framework of mean-field theory the equation for the order-parameter
profile in a spherically-symmetric geometry at the bulk critical point reduces
to an Emden-Fowler problem. We obtain analytic solutions for the surface
universality class of extraordinary transitions in $d=4$ for a spherical shell,
which may serve as a starting point for a pertubative calculation. It is
demonstrated that the solution correctly reproduces the Fisher-de Gennes effect
in the limit of the parallel-plate geometry.
