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Three-Dimensional Stationary Spherically Symmetric Stellar Dynamic ModelsDepending on the Local Energy.  Juergen Batt, Enno Joern, Alexander L. Skubachevskii  The stellar dynamic models considered here are triples (f,rho,U) of threefunctions: the distribution function f=f(r,u), the local density rho=rho(r) andthe Newtonian potential U=U(r), where r:=|x|, u:=|v| ((x,v) in R^3xR^3 are thespace-velocity coordinates), and f is a function q of the local energyE=U(r)+u^2/2. Our first result is an answer to the following question: Given a(positive) function p=p(r) on a bounded interval [0,R], how can one recognize pas the local density of a stellar dynamic model of the given type ("inverseproblem")? If this is the case, we say that p is "extendable" (to a completestellar dynamic model). Assuming that p is strictly decreasing, we reveal theconnection between p and F, which appears in the nonlinear integral equationp=FU[p] and the solvability of Eddington's equation between F and q. Second, weinvestigate the following question ("direct problem"): Which q inducedistribution functions f of the form f=q(-E(r,u)-E0) of a stellar dynamicmodel? This leads to the investigation of the nonlinear equation p=FU[p] in anapproximate and constructive way by mainly numerical methods.  The paper extends preceding work on flat galaxies to the three-dimensionalcase. In particular, the present answer to the extendability problem iscompletely different as in [1]. The present paper also opens the way to furtherexplicit solutions of the Vlasov-Poisson system beyond the classical knownexamples which are for instant given in [4]. Keywords: Vlasov-Poisson system,stationary solutions, numerical approximation, mathematical physic, galaxyastrophysics.

Three-Dimensional Stationary Spherically Symmetric Stellar Dynamic Models DEpending on Local Energy