Stability of nonlinear elliptic systems with distributed parameters and variable boundary data

In this paper nonlinear partial differential equations of the elliptic type with the Dirichlet boundary data are investigated. Some sufficient conditions under which the solutions of considered equations depend continuously on parameters and boundary conditions are proved. The proofs of main results are based on variational methods. In the final part of the paper we give a short survey of the results and methods related to the question of stability of the boundary value problems.