Generic properties of free boundary problems in plasma physics*

We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations,the following alternativeholds: either the shape of the branchof solutions resembles the monotoneone of the model case of the two-dimensional disk, or it is a continuous simple curve without bifurcation points which ends up at a point where the boundary density vanishes. On the otherhand,wededuceageneralcriterionensuringtheexistenceofafreebound- ary in the interior of the domain. Application to a classic nonlinear eigenvalue problem is also discussed.