Abstract
In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the manifold of the states sharing a fixed charge. For non-linearities which are combinations of two competing powers we prove that standing-waves in the ground-state are orbitally stable. We also show the existence of a degenerate minimum and the existence of two positive and radially symmetric minima having the same charge.
Original language | English |
---|---|
Pages (from-to) | 9189-9223 |
Number of pages | 35 |
Journal | Journal of Differential Equations |
Volume | 269 |
Issue number | 11 |
DOIs | |
Publication status | Published - 15 Nov 2020 |
Keywords
- Klein-Gordon equation
- Stability
- Uniqueness
ASJC Scopus subject areas
- Analysis
- Applied Mathematics