On the uniqueness and stability of solutions of two-dimensional plasmastatic problems

Durinq the numerical investiqation of a plasma cylinder in magnetic field of some helical conducting wires in equilibrium, we discuss some questions on the solution, uniqueness and stability in boundary problems with the nonlinear elliptic Grad-Shafranov equation. Some examples of nonunique and unstable solutions are given. A spectral analysis of the linearized equation made possible to determine a restriction of admissible parameter values and to specify iterative methods of solving the problem. The scheme investigation and a general nature of obtained results are typical for a large class of two-dimensional models of static magnetoplasma configurations.