An elliptic problem arising from the unsteady transonic small disturbance equation

We prove a theorem on existence of a weak solution of the Dirichlet problem for a quasilinear elliptic equation with a degeneracy on one part of the boundary. The degeneracy is of a type (''Keldysh type'') associated with singular behavior-blow-up of a derivative-at the boundary. We define an associated operator which is continuous, pseudo-monotone and coercive and show that a weak solution displaying singular behavior at the boundary exists. (C) 1996 Academic Press, Inc.