Sitong Chen, Xianhua Tang, Jiuyang Wei, Normalized solutions to Schrödinger equations with potentials and general nonlinearities

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DOI: 10.23952/jnva.10.2026.6.02

Volume 10, Issue 6, 1 December 2026, Pages 1053-1077

Abstract. We investigate the existence of normalized solutions for the following Schrödinger equation with an $L^2$ -constraint

$-\Delta u+[V(x)+\lambda] u=f(u),\ x\in \mathbb{R}^N,$
$\int_{\mathbb{R}^N}u^2\mathrm{d}x=c,$

where $N\ge3$ , $c>0$ is a prescribed mass, $\lambda\in \mathbb{R}$ arises as a Lagrange multiplier, and $f\in \mathcal{C}(\mathbb{R},\mathbb{R})$ exhibits the $L^2$ -supercritical growth. Without assuming $\mathcal{C}^1$ regularity on $f$ , we establish the existence results in two scenarios concerning $V$ : Non-potential case $V(x) \equiv 0$ and Potential case $V(x) \not\equiv 0$ .

How to Cite this Article:
S. Chen, X. Tang, J. Wei, Normalized solutions to Schrödinger equations with potentials and general nonlinearities, J. Nonlinear Var. Anal. 10 (2026), 1053-1177.