Normalized Multi-peak Solutions to Nonlinear Elliptic Problems

In this article, we establish the existence of positive multi-peak solutions to the following elliptic problem {-Delta v+(lambda+V(x))v=v(p) in Omega, v>0 in Omega, integral(Omega)v(2)dx=p,where Omega is a bounded smooth domain of R-N or the whole space R-N, the exponent p satisfies 1<p<(N+2)/(N-2) for N >= 3 and p>1 for N=1,2. For the case of mass subcritical, mass critical, and mass supercritical, we shall deal with the effect of p on the existence of the solution concentrating at k different points, which belong to either partial derivative Omega or Omega, or R-N.