Bifurcation solutions for a nonlinear Dirac equation

In this paper, we study the following nonlinear Dirac equation (NDE)−i∑k=13αk∂ku+mβu=K(x)|u|p−2u+λu,where u:R3→ℂ4, K∈L∞(R3), m>0 is the mass of the electron, λ∈(−m,m) is an unknown parameter, ħ is Planck’s constant, ∂k=∂∂xk, α1,α2,α3, β are 4 × 4 Pauli–Dirac matrices and p∈(2,83). We present a ne...

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Bibliographic Details
Published inApplied mathematics letters Vol. 134; p. 108306
Main Author Yu, Yuanyang
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.12.2022
Subjects
Bifurcation
Nonlinear Dirac equation
Variational methods
Variational methods
Bifurcation
Nonlinear Dirac equation
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Summary:In this paper, we study the following nonlinear Dirac equation (NDE)−i∑k=13αk∂ku+mβu=K(x)|u|p−2u+λu,where u:R3→ℂ4, K∈L∞(R3), m>0 is the mass of the electron, λ∈(−m,m) is an unknown parameter, ħ is Planck’s constant, ∂k=∂∂xk, α1,α2,α3, β are 4 × 4 Pauli–Dirac matrices and p∈(2,83). We present a new approach which is based on some prior estimates, and show that the spectrum point m is a bifurcation point for equation (NDE) by using variational methods.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2022.108306