NORMALIZED SOLUTIONS FOR THE CHERN-SIMONS-SCHRODINGER EQUATION IN R2

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 submanifold of S-r(c), we prove that for certain c > 0, I has a critical point on Sr(c). After that, we get an H-1-bifurcation result of our problem. Moreover, by using a minimax procedure, we prove that there are infinitely many critical points of I restricted on S-r(c) for any c epsilon (0, 4 pi/root p-3).