GENERAL STUDY OF A KIND OF SINGULAR STIFF PROBLEMS

The problem studied in this Note is a classical problem of singular pe rturbation which occurs in several domains, for instance in shell theo ry (see [3]). It is shown first that the problem may be split in two i ndependent problems and come down to the case when the ''abyss'' (''go uffre'' in french) introduced by Sanchez-Palencia [3] is reduced to th e zero element (proposition 1). Then a topology is introduced and a co nvergence result is proved for this problem under no other hypotheses on the right hand member F (v) than linearity and continuity (proposit ion 2). This result extends some already known results for particular F (v).