  A semilinear singularly perturbed reaction-diffusion equation with Dirichlet
boundary conditions is considered in a convex unbounded sector. The singular
perturbation parameter is arbitrarily small, and the "reduced equation" may
have multiple solutions. A formal asymptotic expansion for a possible solution
is constructed that involves boundary and corner layer functions. For this
asymptotic expansion, we establish certain inequalities that are used in a
subsequent paper to construct sharp sub- and super-solutions and then establish
the existence of a solution to a similar nonlinear elliptic problem in a convex
polygon.
