This paper proves that there is
a (weak) solution u (not necessarily unique) to the generalized Dirichlet problem
(with null boundary data) for the equation Au + pu = h. Here A is a strongly and
uniformly elliptic operator of order 2m on a bounded open set Ω ⊆ Rn. Also A is
“normal”: roughly, AA∗= A∗A. The functions p and h are bounded and continuous,
but are allowed to depend on x(x ∈ Ω),u, and the generalized derivatives of
u up to order m. The values of p are restricted to lie in a closed disk of
the complex plane which contains the negative of no weak eigenvalue of
A.
