Nonlocal problems for the Vlasov-Poisson equations in an infinite cylinder

The Vlasov-Poisson equations with an external magnetic field in an infinite cylinder for a two-component high-temperature plasma with initial conditions on the distribution densities of charged particles and nonlocal boundary condition on the electric field potential are considered. For sufficiently small initial distribution densities, the existence and uniqueness of a classical solution for which the distribution densities of charged particles are supported on an inner cylinder are proved.