Singularly perturbed loads for a nonlinear traction boundary value problem on a singularly perturbed domain

This paper treats the equilibrium of a family of linearly elastic bodies in $n$ dimensional Euclidean space containing a small hole of arbitrary shape of size $\epsilon$ with the traction on the hole depending nonlinearly on the displacement and depending in a singular way on $\epsilon$. Under suitable assumptions we illustrate that this problem has a solution for small $\epsilon$ and we analyze its behaviour as $\epsilon$ tends to 0. Our approach is different from standard methods of asymptotics.