Existence and asymptotic behavior of solutions for Choquard equations with singular potential under Berestycki-Lions type conditions

We prove the existence and asymptotic behavior of solutions to the following problem: [GRAPHICS] where g(x) := mu |x| is called the Coulomb potential, g(x) := ss |x|2 is called the Hardy potential (the inverse-square potential). mu, ss > 0 are parameters, Ia : RN -. R is the Riesz potential. Moreover, the nonlinearity f satisfies Berestycki-Lions type conditions which are introduced by Moroz and Van Schaftingen (Trans. Amer. Math. Soc. 367 (2015) 6557-6579). When mu. (0, a(N - 2)/2( a + 1)) and ss. (0, a(N - 2)2/4(2+ a)), under some mild assumptions on V, we establish the existence and asymptotic behavior of solutions. Particularly, our results extend some relate ones in the literature.