The Schrödinger-Poisson system on $\mathbb R^3$ with multiple weighted critical exponents

We are concerned with the Schrödinger-Poisson system with the nonlinearity involving multiple weighted critical exponents. The weighted critical exponent may be the Hénon-Sobolev, the Sobolev or the Hardy-Sobolev critical exponent. Moreover, the potentials contained in the Schrödinger-Poisson system are weights of power type, which may be singular at origin or unbounded at infinity. The existence of ground state solutions for the Schrödinger-Poisson system is obtained.