Radiation conditions and the exterior Dirichlet problem for a class of higher order elliptic equations

Denote by L a second order strongly elliptic operator in the Euclidian p-space $\text{R}$^p, and by P some real polynomial in one variable. First the wholespace-problem for the equation P(L)u = f is considered and asymptotic conditions are derived which yield an existence and uniqueness theorem. Then for the Dirichlet problem in some exterior domain G ? $\text{R}$^p a “Fredholm alternative theorem” is proved.