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In this paper, we consider two bounded open subsets of Ω  i   and Ω  o   of R  n   containing 0 and a (nonlinear) function  G   o   of ∂Ω  o  ×R  n   to R  n  , and a map  T  of ]1-(2/ n ),+∞[ times the set  M   n  (R) of  n ×  n  matrices with real entries to  M   n  (R), and we consider the problem

A singularly perturbed nonlinear traction boundary value problem for linearized elastostatics. A functional analytic approach