Normalized solutions for L2-supercritical Schrödinger equations

This paper is concerned with the following $L^2$-supercritical Schrödinger equation $\left(\begin{array}{c}-\Delta u-\lambda u=f\left(u\right),\\ {\int }_{R^N}{u}^{2}dx=c,\end{array}\right)$where $N\ge 3$, $f\in C(R,R)$, $c>0$ is a given mass and $\lambda \in R$ will arise as a Lagrange multiplier depending on the solution $u\in H^1\left(R^N\right)$. By introducing new weak $L^2$-supercritical conditions on $f$, we develop robust arguments to establish the existence of normalized solutions to the above equation. Our result complements the ones of Chen and Tang (2024).