Normalized solutions of $L^2$-supercritical NLS equations with periodic potentials and localized nonlinearities

In this paper, we study the existence of normalized solutions to the following $L^2$-supercritical nonlinear Schrödinger equation with a periodic potential \[ \begin{dcases} -Δu +V (x)u + λu=χ_{Ω}(x)f(u)\quad \text{in }\mathbb{R}^N, u>0 \quad \text{in} \ \mathbb{R}^N, \int_{\mathbb{R}^N}\abs