实Clifford分析中三类高阶奇异积分及其非线性微分积分方程

本文第一部分借助于高阶异积分的Ｈａｄａｍａｒｄ主值的思想以及归纳法的思想，在证明了６个引理的基础上讨论实Ｃｌｉｆｆｏｒｄ分析中三类高阶异积分的归纳定义，Ｈａｄａｍａｒｄ主值的存在性，递推公式，计算公式以及高阶奇异积分在Ｈａｄａｍａｒｄ主值意义下的１２个微分公式，受多复变中解析函数积分表示式多样笥的，本文采用的算子的积分表达式就与个公式和微分公式都十分乘法本文第二部分在引进并证明了Ｈｉｌｅ引理型的基

Three Kind High Order SingularIntegrals and Nonlinear Differentio-Integral Equation in the Real Clifford Analysis

In the first part of this paper, by the think of Hadamard principal value andthe think of induction, in view of prove the six lemma, we consider induce define, existence ofHadamard principal value, recurrence formula, compute formula and twelve differefltial formulafor three kind high order singular integrals in real Clifford analysis. Deal of enlightenment frommake varied for integral expression of function in several complex variables, in the paper adoptexpression of integral operators differ from illtegral expression for regular function in real Cliffordanalysis, thus in this paper we give the ten-five compute formulas and differential formulasbecome very simple. In the second part of this paper, in view of design and proof for Hile's typelemma, applying the method of integral equations and Schauder fixed-point theorem (principle ofcontracting mapping), the existence (uniqueness) of solution for the nonlinear differentio-integralequation contain three find high order singular integrals in real Clifford analysis is proved.