Virtual Community of Pathological Anatomy (University of Castilla La Mancha)· 2020
Normalized ground states for the NLS equation with combined nonlinearities: The Sobolev critical case
- 408citations
- 2020year
Short summary
This paper proves the first existence results for normalized ground states of the Sobolev critical nonlinear Schrödinger equation (NLSE) in the whole space R^N (N>=3).
AI-generated from the title and abstract; the full text is not read.
Key points
- First existence results for normalized ground states of the Sobolev critical NLSE in R^N (N>=3).
- Considers the equation -Δu=λu+μ|u|q−2u+|u|2javax.xml.bind.JAXBElement@4d419c48−2u with prescribed mass ∫|u|^2=a^2.
- Analyzes combined power nonlinearities with L2-subcritical, L2-critical, or L2-supercritical perturbations.
- Provides existence/non-existence and stability/instability results.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study existence and properties of ground states for the nonlinear Schrödinger equation with combined power nonlinearities −Δu=λu+μ|u|q−2u+|u|2javax.xml.bind.JAXBElement@4d419c48−2uin RN, N≥3, having prescribed mass ∫RN|u|2=a2, in the Sobolev critical case. For a L2-subcritical, L2-critical, of L2-supercritical perturbation μ|u|q−2u we prove several existence/non-existence and stability/instability results. This study can be considered as a counterpart of the Brezis-Nirenberg problem in the context of normalized solutions, and seems to be the first contribution regarding existence of normalized ground states for the Sobolev critical NLSE in the whole space RN.
The authors' abstract, as published at the source. Virtual Community of Pathological Anatomy (University of Castilla La Mancha), 2020 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Mathematical Physics
Mathematical PhysicsMathematics