Polynomial solutions of quasi-homogeneous partial differential equations

被引：0

作者：

LUO Xuebo ZHENG Zhujun Institute of Applied Mathematics

Institute of Mathematics

机构：

来源：

Science China Mathematics | 2001年 / 09期

基金：

中国国家自然科学基金;

关键词：

quasi-homogeneous partial differential operator; polynomial solution; dimension of the space of solution; method of analytic number theory;

D O I：

暂无

中图分类号：

O175 [微分方程、积分方程];

学科分类号：

070104 ;

摘要：

By means of a method of analytic number theory the following theorem is proved. Let p be a quasi-homogeneous linear partial differential operator with degree m, m > 0, w.r.ta dilation{δτ}τ<0 given by ( a1, …, an). Assume that either a1, …,an are positive rational numbers or m =ajaj for some a = (a1,…,an)∈In+. Then the dimension of the space of polynomial solutions of the equation p[u] =0 on Rn must be infinite.

引用

页码：1148 / 1155

页数：8

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