On semi-classical limits of ground states of a nonlinear Maxwell-Dirac system
Yanheng, Ding · Tian, Xu
Original · EN
We study the semi-classical ground states of the nonlinear Maxwell-Dirac system: { aligned &·(iℏ∇+ q(x)(x)) w-a w -ωw - q(x)ϕ(x) w = P(x)g(w) w &-Δϕ=q(x)w² &-ΔAₖ=q(x)(αₖ w)· wk=1,2,3 aligned. for x∈³, where is the magnetic field, ϕ is the electron field and q describes the changing pointwise charge distribution. We develop a variational method to establish the existence of least energy solutions for ℏ small. We also describe the concentration behavior of the solutions as ℏ→ 0.
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