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In this paper, we study the existence of normalized solutions to thefollowing nonlinear Schr\"{o}dinger equation \begin{equation*} \left\{\begin{aligned} &-\Delta u=f(u)+ \lambda u\quad \mbox{in}\ \mathbb{R}^{N},\\&u\in H^1(\mathbb{R}^N), ~~~\int_{\mathbb{R}^N}|u|^2dx=c, \end{aligned} \right.\end{equation*} where $N\ge3$, $c>0$, $\lambda\in \mathbb{R}$ and $f$ has aSobolev critical growth at infinity but does not satisfies theAmbrosetti-Rabinowitz condition. By analysing the monotonicity of the groundstate energy with respect to $c$, we develop a constrained minimizationapproach to establish the existence of normalized ground state solutions forall $c>0$.

Normalized ground states for nonlinear Schr\"{o}dinger equations with general Sobolev critical nonlinearities