Infinitely many normalized solutions for Schrödinger equations with local sublinear nonlinearity

Abstract In this article, we investigate the following Schrödinger equation: − Δ u = h ( x ) g ( u ) + λ u in R N , ∫ R N ∣ u ∣ 2 d x = a u ∈ H 1 ( R N ) , \left\{\begin{array}{ll}-\Delta u=h\left(x)g\left(u)+\lambda u\hspace{1.0em}& \hspace{-0.2em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{N},\\ \mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}{| u| }^{2}\hspace{0.1em}\text{d}\hspace{0.1em}x=a\hspace{1.0em}& u\in {H}^{1}\left({{\mathbb{R}}}^{N}),\end{array}\right. where N ≥ 3 N\ge 3 , a > 0 a\gt 0 , and λ ∈ R \lambda \in {\mathbb{R}} arises as a Lagrange multiplier. Assuming that the sublinear nonlinearity