Multiple normalized standing-wave solutions to the scalar non-linear Klein-Gordon equation with two competing powers

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1 Citation (Scopus)

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 languageEnglish
Pages (from-to)9189-9223
Number of pages35
JournalJournal of Differential Equations
Volume269
Issue number11
DOIs
Publication statusPublished - 15 Nov 2020

Keywords

  • Klein-Gordon equation
  • Stability
  • Uniqueness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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