Iteration methods for nonlinear problems

The methods of successive displacements or relaxation methods are investigated for a class of nonlinear problems. In particular it is shown that these methods are applicable to a large class of nonlinear problems arising from variational problems which yield elliptic equations. Constructive existence and uniqueness theorems are presented for the discrete problem and criteria are given for a practical method of obtaining solutions. The example of a discrete Plateau problem is used to illustrate the feasibility of the results. The processes are also shown to apply to uniformly elliptic problems.