Virtual Community of Pathological Anatomy (University of Castilla La Mancha)· 2020
Normalized ground states for the NLS equation with combined nonlinearities
- 418citations
- 2020year
Short summary
This paper proves existence and stability/instability results for ground states of the nonlinear Schrödinger equation with combined power nonlinearities, specifically when the nonlinearities have different characters relative to the L2-critical exponent.
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Key points
- Establishes existence and properties of ground states for NLS equation with combined power nonlinearities and prescribed mass.
- Analyzes cases where nonlinearities have different characters relative to the L2-critical exponent.
- Demonstrates substantial differences from purely subcritical or supercritical situations.
- Provides new criteria for global existence and finite-time blow-up in the associated dispersive equation.
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|p−2uin RN, N≥1, having prescribed mass ∫RN|u|2=a2. Under different assumptions on q0 and μ∈R we prove several existence and stability/instability results. In particular, we consider cases when [Formula presented] i.e. the two nonlinearities have different character with respect to the L2-critical exponent. These cases present substantial differences with respect to purely subcritical or supercritical situations, which were already studied in the literature. We also give new criteria for global existence and finite time blow-up in the associated dispersive equation.
The authors' abstract, as published at the source. Virtual Community of Pathological Anatomy (University of Castilla La Mancha), 2020 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics