Heng Yang

Normalized solutions for the nonlinear Schrödinger equation with potential and Sobolev critical nonlinearity

This paper investigates the existence of normalized solutions to the following Schrödinger equation $$ \begin{cases} -\Delta u + [V(x) + \lambda] u = \mu |u|^{q-2}u + |u|^{2^*-2}u, & x\in \mathbb{R}^N, \\ \int_{\mathbb{R}^N}u^2\mathrm{d}x = c, \end{cases} $$ where $N\ge 3,$ $2 < q < 2^*=\frac{2N}{N-2}$, $c > 0$ is a pr...