Rui-Shu Liu

Normalized solutions to 1-Laplace equations with critical growth term

We study normalized solutions to the 1-Laplace equation \[ -\mbox{div}\left(\frac{Du}{|Du|}\right)+\lambda \frac{u}{|u|}=f(u)+|u|^{1^*-2}u,\quad\mbox{in}~ \mathbb{R}^N \] subject to the constraint $\int_{\mathbb{R}^N}|u| \, \mbox{d}x=m$, where $N\geq2$, $1^*=\frac{N}{N-1}$ is the critical Sobolev exponent for the embed...