Normalized Ground State Solutions for Critical Growth Schrödinger Equations

This paper investigates the existence of solutions with a prescribed L 2 -norm for the nonlinear Sobolev critical Schrödinger equation: - Δ u + λ u = g ( u ) + | u | 2 ∗ - 2 u , in R N , ∫ R N | u | 2 d x = a , u ∈ H 1 ( R N ) , where N ≥ 3 , a > 0 , 2 ∗ = 2 N 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.