REMARKS ON NORMALIZED GROUND STATES OF SCHRÖDINGER EQUATION WITH AT LEAST MASS CRITICAL NONLINEARITY

Abstract

We are concerned with the nonlinear Schrödinger equation

$ \begin{equation*}-\Delta u+\lambda u=g(u)\text{ in }\mathbb{R}^{N}\text{, }\lambda \in\mathbb{R}, \end{equation*} $ with prescribed \begin{document}$L^{2}$\end{document}-norm \begin{document}$\int_{\mathbb{R}^{N}}u^{2}dx=\rho ^{2}$\end{document}. Under general assumptions about the nonlinearity which allows at least mass critical growth, we prove the existence of a ground state solution to the problem via a clear constrained minimization method.