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This paper is concerned with the qualitative properties of the positiveground state solutions to the nonlocal Choquard type equation on a ball $B_R$.First, we prove the radial symmetry of the positive ground state solutions byusing Talenti's inequality. Next we develop Newton's Theorem and then resort tothe contraction mapping principle to establish the uniqueness of the positiveground state solutions. Finally, by constructing cut-off functions and applyingenergy comparison method, we show the convergence of the positive ground statesolutions as $R\to \infty$. Our results generalize and improve the existingones in the literature.

Uniqueness, symmetry and convergence of positive ground state solutions of the Choquard type equation on a ball