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We consider the two-dimensional nonlinear Dirichlet problem -Au=Xe ', y2, u= y O2, where y--(y,y_), A is the Laplacian operator, 2 is a simply connected region bounded by a smooth closed Jordan curve, the boundary data q, is continuous and X is positive. Our primary concern is with obtaining the large norm (second) solution for X tending to 0+. This is accomplished by obtaining an asymptotic solution which is used as a first approximation for a modified Newton's method. In this paper we examine the implicit constraints previously required for q--=0 and extend the results to the case of nonzero boundary data.

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