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- Title
Interactions in the Lorentz force equation.
- Authors
Bereanu, Cristian
- Abstract
In this paper we consider for arbitrary μ ∈ R the Lorentz force equation q ′ 1 - | q ′ | 2 ′ + μ q = - ∇ q V - ∂ W ∂ t + q ′ × curl q W , with a Kepler type electric potential V + μ 2 | q | 2 and a smooth magnetic potential W which are T-periodic in time. We show that two fundamentally different cases occurs: the case μ = 0 and the case μ ≠ 0. In both cases we show that under different types of interactions at infinity between the electric and the magnetic potentials, we have that the Lorentz force equation has a sequence (q n) of T-periodic solutions such that I (q n) → + ∞ as n → ∞ , where I is the action functional associated to the Lorentz force equation. To prove our main result–using the Lusternik–Schnirelman category and Ekeland's variational principle—we develop a Lusternik–Schnirelman strategy for the nonsmooth action functional associated to the Lorentz force equation.
- Subjects
LORENTZ force; VARIATIONAL principles; EQUATIONS
- Publication
Calculus of Variations & Partial Differential Equations, 2024, Vol 63, Issue 2, p1
- ISSN
0944-2669
- Publication type
Article
- DOI
10.1007/s00526-023-02635-y