A function theoretic method forΔ 4 2 u+Q(x)u=0

Summary The approach used in this paper generalizes Colton's treatment [4] of certain second order elliptic equations in four independent variables to the fourth order case. This method is essentially a function theoretic one that is based on the earlier work of Tjong [11]. An integral operator is found that permits one to construct a complete family of solutions with respect to uniform convergence in compact sets of R4. Consequently, one is provided with a useful numerical procedure for solving the associated boundary value problems.