Abstract
where Sz c R” (n 2 1) is bounded with smooth boundary aQ. Readers interested in the derivation of the problem are referred to the work by Bebernen [l], particularly Section 2. Relevant work on the analysis of this problem has been done by Brown et al. [2], Shivaji [3-61, Hastings and McLeod [7], Sattinger [8], Parks [9] and Tam [lo]. Clearly u = 0 is a solution of (1 .l), when 2 = 0. It follows from the contraction mapping theorem that (l.l), always has a solution for A sufficiently small. Moreover, let
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