Nonlinear Dirac equations with Coulomb-type potentials and nonlinearities resonating at essential spectrums
Published online by Cambridge University Press: 15 April 2018
Abstract
We consider the nonlinear Dirac equation
The potential function V satisfies the conditions that the essential spectrum of the Dirac operator is and this Dirac operator has infinitely many eigenvalues in (−1, 1) accumulating at 1. This potential function V may change sign in ℝ3 and contains the classical Coulomb potential V (x) = −γ/|x| with γ > 0 as a special case. The nonlinearity F satisfies the resonance-type condition lim. Under some additional conditions on V and F, we prove that this equation has infinitely many solutions.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 148 , Issue 4 , August 2018 , pp. 713 - 730
- Copyright
- Copyright © Royal Society of Edinburgh 2018
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