一类重调和方程边值问题解的奇点可去性

Removability of Singularities of Solutions of Polyharmonic Equations Boundary Value Problem

给出了一类重调和方程边值问题解的表示式,研究了其解的奇点可去性,利用判断反常积分收敛性的方法对解的表示式作了敛散性分析,给出了该类方程在限定条件下的具体表达式,研究了相应的解的积分表达式.将函数项幂次的取值范围在实数域上分为3段,分别讨论了每种情形下相应积分式的敛散性,得出了其在不同参数范围下解的奇点可去性.

Methods for discriminating convergence and divergence of an improper integral was utilized to analysis the convergence and divergence of the representation formula of solutions of polyharmonic equations boundary value problem,The concrete formula of the equation was given in certain restricted conditions,The corresponding integral expressions were studied,Furthermore,the power of functions was divided into three parts in real number field and the convergence and divergence of corresponding integral expressions were analyzed separately in each section,Based on the above discussion,the study shows that the integral expressions of solutions are convergent if the power is greater than a certain critical value and the singularity is removable,while they are divergent if the power is less than the critical value and the singularity is nonremovable.