Ground state solutions for the Chern-Simons-Schrodinger equations with general nonlinearity

We consider the nonlinear Chern-Simons-Schrodinger equations with general nonlinearity -Delta u + wu + (integral(infinity)(vertical bar x vertical bar) h(s)/s u(2)(s)ds) u + h(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) u = f (u), x is an element of R-2, where h(s) = integral(s)(0) (r/2)u(2)(r)dr = (1/4 pi) integral(Bs) u(2)(x) dx and w > 0. With the condition , we obtain the ground state solution of the Nehari-Pohozaev type. Based on the result, by the Jeanjeans monotonicity trick, we also get a least energy solution. For the case , the existence of ground state solution is proved by the diagonal method. We generalize the existence results.