1. Introduction. The quasi-linear elliptic partial differential equation to be studied here has the form
(1.1) Δu = − F(P,u).
Here Δ is the Laplacian while F(P,u) is a continuous function of a point P and the dependent variable u. We shall study the Dirichlet problem for (1.1) and will find that the usual formulation must be modified by the inclusion of a parameter in the data or the differential equation, together with a further numerical condition on the solution.