N-DIMENSIONAL MULTIPLE NON-HOMOGENEOUS HARMONIC EQUATION AND ITS BOUNDARY INTEGRAL EQUATION
N维多重非齐次调和方程及其边界积分方程

In this paper, the $n$-dimensional multiple non-homogeneous harmonic equation ${\it \Delta}^{(k)}u=f(x),x\in\mbox{\boldmath $R$}^{n}$, is considered. Firstly, the fundamental solution and its recurrence formulae are given. Then some fundamental integral relations are presented, specially, for multiple harmonic function. Under the assumption that non-homogeneous term $f(x)$ is $m$-degree harmonic, the integral term in domain is shifted boundary integral, and hence the boundary integral equation without integral in domain is obtained. Finally, the error and convergence analysis is discussed by Taylor polynomial approximation of non-homogeneous term $f(x)$.