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A constraint variational problem arising in stellar dynamics

We use the compactness result of A. Burchard and Y. Guo to analyze the reduced 'energy' functional arising naturally in the stability analysis of steady states of the Vlasov-Poisson system (cf. Sanchez and Soler, to appear, and Hadzic, 2005). We consider the associated variational problem and present a new proof that puts it in the general framework for tackling the variational problems of this type, given by Y. Guo and G. Rein (cf. Rein, 2005 and Rein, 2002).