The defining boundary conditions and the degenerate problem for elliptic boundary-value problems with a small parameter in the highest derivatives

Abstract

For an elliptic equation with a small parameter multiplying the highest derivatives one considers a boundary-value problem such that some of the orders of the last p boundary conditions are congruent modulo 2p (here 2p is the difference between the orders of the perturbed and the non-perturbed equations). In the case when no three of them are congruent modulo 2p, associated boundary conditions are obtained and results on the asymptotic expansion are established.