The existence of ground state normalized solution for mass supercritical modified Kirchhoff equation

In this paper, we focus on the existence of ground state solution with prescribed L2-norm for the following modified Kirchhoff problem: −a+b∫RN|∇u|2dxΔu−uΔ(u2)−λu=|u|p−2u,x∈RN,where N=2,3, a,b>0 are constants, p∈4+4N,2∗, 2∗=6 if N=3, and 2∗=+∞ if N=2. By employing a novel scaling method, we establish the existence of ground state normalized solutions for the above problem. Our result is new for the mass supercritical case 4+4N<p≤2∗, notably for the case p=2∗.