Sign-changing multi-bump solutions for the Chern-Simons-Schrodinger equations in R2

In this paper we consider the nonlinear Chern-Simons-Schrodinger equations with general nonlinearity -Delta u +lambda V (vertical bar x vertical bar)u+ (h(2)(vertical bar x vertical bar)/vertical bar x vertical bar(2) +integral(infinity)(vertical bar x vertical bar)h(s)/s u(2)(s) ds) u = f(u), x is an element of R-,(2) where lambda> 0, V is an external potential and h(s) = 1/2 integral(s)(0) ru(2)(r)dr = 1/4 pi integral(Bs) u(2) (x) dx is the so-called Chern-Simons term. Assuming that the external potential V is nonnegative continuous function with a potential well Omega := intV(-1) (0) consisting of k + 1 disjoint components Omega(0), Omega(1), Omega(2) ... , Omega(k), and the nonlinearity f has a general subcritical growth condition, we are able to establish the existence of signchanging multi-bump solutions by using variational methods. Moreover, the concentration behavior of solutions as lambda ->+infinity are also considered.