Asymptotic profile of ground states for the Schrödinger-Poisson-Slater equation

Abstract

We study the Schrödinger-Poisson-Slater equation $$-\Delta u+u+\lambda (I_2\ast |u{|}^2)u=|u{|}^{p-2}u\text{in R3},$$ where $p\in (3,6)$ and $\lambda >0$. By using direct variational analysis based on the comparison of the ground state energy levels, we obtain a characterization of the limit profile of the positive ground states for $\lambda \to \infty$.

7 pages