Normalized Sign‐Changing Solutions for the Nonlinear Schrödinger Equation With a Mass‐Critical Perturbation

ABSTRACT We investigate the mass‐critical perturbed nonlinear Schrödinger equation with a prescribed mass and establish the existence of sign‐changing normalized solutions in noncompact settings for . Additionally, we analyze the asymptotic behavior of these normalized solutions as the perturbation parameter approaches zero. This work is an extension of Soave's article (J. Differential Equations (2020)) where the focus was on radial normalized solutions. In contrast, the normalized solutions we obtain are nonradial.