Although the experimental foundation for the existence of boson stars is completely lacking, on the theoretical and mathematical front, boson stars are well studied. Recent work includes a mathematical approach in terms of large and small data , followed up by studying singularity formation  and uniqueness [88, 150] for a certain boson star equation. In Ref. , they study radial solutions of the semi-relativistic Hartree type equations in terms of global well-posedness. Ref.  demonstrates stationarity of time periodic scalar field solutions.
Beyond just existence, however, boson stars are often employed mathematically to study dynamics. Here, we concentrate on a few of these topics that have attracted recent interest.
Living Rev. Relativity 15, (2012), 6
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