On the mass concentration of L2-constrained minimizers for a class of Schrödinger-Poisson equations
Abstract
In this paper, we study the mass concentration behavior of positive solutions with prescribed L2-norm for a class of Schrödinger-Poisson equations in R3-Δu-μu+ϕuu-|u|p-2u=0,x∈R3,μ∈R,-Δϕu=|u|2,where p∈(2,6). We show that positive solutions with prescribed L2-norm as which tends to 0 (in some cases) or to +∞ (in others), behave like the positive solution of Schrödinger equation -Δu+u=|u|p-2u in R3.
- Publication:
-
Zeitschrift Angewandte Mathematik und Physik
- Pub Date:
- June 2018
- DOI:
- 10.1007/s00033-018-0963-4
- Bibcode:
- 2018ZaMP...69...66Y
- Keywords:
-
- Normalized solutions;
- L2-subcritical;
- L2-supercritical;
- Mass concentration;
- Schrödinger–Poisson equation;
- 35J60;
- 35A15