Normalized Solutions for a Kirchhoff Equation with Potential in $\mathbb{R}^3$ (Journal of Mathematical Study, 2024)
In this paper, for given mass $c>0,$ we study the existence of normalizedsolutions to the following nonlinear Kirchhoff equation  $$\begin{cases} (a+b\int_{\mathbb{R}^3}[| abla u|^2+V(x)u^2]dx)[-\Delta u+V(x)u]=\lambda u+\mu|u|^{q-2}u+|u|^{p-2}u, \ \ \ {\rm in}\ \ \mathbb{R}^3, \\ \int_{\mathbb{R}^3}|u|^2dx=c^2, \end{cases}$$where $a>0, b>0, λ∈\mathbb{R},$ $5