J. Batt et K. Fabian, STATIONARY SOLUTIONS OF THE RELATIVISTIC VLASOV-MAXWELL SYSTEM OF PLASMA PHYSICS, Chinese annals of mathematics. Ser. B, 14(3), 1993, pp. 253-278
The authors consider the stationary relativistic coupled system consis
ting of Vlasov's equation for the distribution function of charged par
ticles and Maxwell's equations for the electric and magnetic fields of
a plasma. With different tools of nonlinear functional analysis the e
xistence of solutions is proved, in which, according to different geom
etries and symmetries, the distribution function depends on one, two o
r three independent integrals of the motion.