Stationary solutions of the Vlasov–Poisson system with an external magnetic field for a two-component high-temperature plasma in the half-space

We consider the first mixed problem for the Vlasov–Poisson equations in the half-space describing the evolution of the density distribution of ions and electrons in a high-temperature plasma with an external magnetic field. We construct a stationary solution with a support that is compactly contained in the domain under сonsideration.