Asymptotical analysis of the Stiff problem with Singularity on the exterior domain

In this paper the Stiff problem (A) with Singularity on the exterior domain is reduced to the functional Variational problem(B).
Using an asymptotical expansion introduced by Lions, we then discuss the Solution of (B), i.e., letting the solution of (B) be a power series expansion in ε:
u_ε=((u^-1)/(ε))+u⁰+εu¹+ε²u²+…
and Substituting u_ε into (B) , is obtoined a sequence of cyclic formulas of coefficients u^-1,u⁰,u¹,u²,….