NONREGULAR BOUNDARY VALUE PROBLEMS WITH A PARAMETER

In this paper, we discuss boundary value problems for a class of nonlinear elliptic equations with data on a boundary surface. We denote by y the unknown function which is supposed to take its values in We assume that only some components of y are given on the whole boundary surface implying the designation of nonregular boundary value problems. To derive an interesting necessary condition for the solvability of our original problem, we construct an appropriate Cauchy problem for nonlinear elliptic equations which we solve by making use of a parameter which is small enough.