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.