Infinitely many sign-changing normalized solutions for nonlinear scalar field equations

We study the existence of infinitely many sign-changing solutions to the following nonlinear scalar Schrödinger equation $-\Delta u+\lambda u=f\left(u\right)\text{in}{R}^N$with a prescribed mass ${\int }_{R^N}{\left|u\right|}^{2}dx=a.$ Here $f\in C^1(R,R)$, $a>0$ is a given constant and $\lambda \in R$ is an unknown parameter appearing as a Lagrange multiplier. Jeanjean and Lu have established the existence of infinitely many sign-changing normalized solutions in [Nonlinearity 32 (2019), no. 12, 4942–4966] and [Calc. Var. Partial Differential Equations 59 (2020), no. 5, Paper No. 174, 43 pp.] for $N=4$ or $N\ge 6$. After fully utilizing the properties of positive solutions given by Jeanjean,Zhang and Zhong[J. Math. Pures Appl. (9) 183 (2024), 44–75], we give an alternative approach and extend the existence of infinitely many sign-changing normalized solutions to all $N\ge 2$.