Abstract:

In this paper, we consider the following logarithmic Schrödinger equation:

\begin{equation*}

-\Delta u+\omega u =u\log|u|^2,~~ u\in H^1(\mathbb{R}^N),

\end{equation*}

where $N\geq3$, and $\omega>0$ is a constant. With an auxiliary equation, we obtain the existence of normalized solutions by using the constrained variational method.

Key words: Logarithmic Schr?dinger equation, Normalized solution, Constrained variational method , Minimization problem