Resumen de Normalized Ground State Solutions for Critical Growth Schrödinger Equations

Song Fan, Gui-Dong Li

• This paper investigates the existence of solutions with a prescribed L2-norm for the nonlinear Sobolev critical Schrödinger equation:

  −u + λu = g(u) + |u| 2∗−2u, in RN , RN |u| 2dx = a, u ∈ H1(RN ), where N ≥ 3, a > 0, 2∗ = 2N N−2 denotes the critical Sobolev exponent, g belongs to the continuous function space C(R), and the parameter λ serving as a Lagrange multiplier. We employ the Sobolev subcritical approximation method to establish the existence of normalized ground state solutions for this particular class of Schrödinger equations with critical growth.