Serrin-type Overdetermination in Scaling Limits: Sharp Existence and Asymptotic Behavior of Quasi-linear Schrödinger Energy Ground States

Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong

This paper establishes optimal existence results and limiting profiles for energy ground states of the quasi-linear Schrödinger equation $$ -Δu - Δ(|u|^{2})u + λu = |u|^{p-2}u \qua…