In this paper, we study the existence and multiplicity of solutions with a prescribed L-2-norm for a class of nonlinear Chern Simons Schrodinger equations in R-2 where To get such solutions we look for critical points of the energy functional on the constraints When p = 4, we prove a sufficient condition for the nonexistence of constrain critical points of I on S-r(c) for certain c and get infinitely many minimizers of I on Sr(8 pi). For the value p epsilon (4, +infinity) considered, the functional I is unbounded from below on Sr(c). By using the constrained minimization method on a suitable s...
