As usual in mathematical physics, the boundary conditions constitute an important part of the whole problem, and their influence on the solutions is not easy to foresee. This is connected with the fact that the boundary conditions for the problem of stellar structure cannot be imposed at one end of the interval [0, M] only but rather are split into some that are given at the centre and some near the surface of the star. The central conditions are simple, whereas the surface conditions implicate observable quantities and a completely different, much more complicated transport equation. It is therefore advisable to get some feeling about their influence on the stellar structure. We discuss these problems for the case of complete equilibrium.