The energy level transition for nonlinear Kirchhoff equation under a perturbation of potential

In this paper, we study the energy level transition behavior for the nonlinear Kirchhoff equation with a potential and a pure power nonlinearity. The potential function is assumed to be a perturbation of a positive constant. Under a negative perturbation, the persistence for ground state solution is...

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Bibliographic Details
Published inAnnals of physics Vol. 475; p. 169949
Main Authors Li, Baihong, Wei, Yuanhong
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2025
Subjects
Bound state
Energy level transition
Global compactness
Kirchhoff equation
Linking theorem
Global compactness
Kirchhoff equation
Bound state
Linking theorem
Energy level transition
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Summary:In this paper, we study the energy level transition behavior for the nonlinear Kirchhoff equation with a potential and a pure power nonlinearity. The potential function is assumed to be a perturbation of a positive constant. Under a negative perturbation, the persistence for ground state solution is demonstrated. It is also proved that a positive perturbation excludes the ground state solution while ensuring the existence of the bound state solution with high energy. Our approach is based on the variational method, aided by global compactness and linking theorem.
ISSN:0003-4916
DOI:10.1016/j.aop.2025.169949