Normalized solutions for critical growth Schrödinger equations with nonautonomous perturbation.

This paper is dedicated to investigating the existence of solutions characterized by a predefined L 2 -norm in the context of the nonlinear Sobolev critical Schrödinger equation − Δ u + λ u = | u | 2 ∗ − 2 u + V (x) | u | p − 2 u , in R N , ∫ R N u 2 d x = a 2 , u ∈ H 1 (R N). Here, N ≥ 3 , a > 0 and 2 < p < 2 ∗ , where 2 ∗ = 2 N N − 2 represents the critical Sobolev exponent. It is worth noting that the parameter λ functions as a Lagrange multiplier within this framework. [ABSTRACT FROM AUTHOR]