Polynomial solutions of quasi-homogeneous partial differential equations

被引：0

作者：

Luo, XB ^{[1
]}

Zheng, ZJ

机构：

[1] Northwestern Polytech Univ, Inst Appl Math, Xian 710072, Peoples R China

[2] Henan Univ, Inst Math, Kaifeng 475001, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY | 2001年 / 44卷 / 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：

10.1007/BF02877432

中图分类号：

O29 [应用数学];

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. t a dilation {delta(T)}(T<0) given by (a(1),(...), a(n)). Assume that either a(1), (...), a(n) are positive rational numbers or m = Sigma(jsimilar or equal to1) (n)(alphajalphaj) for some alpha =(alpha1, (...), alpha(n)) is an element of I-+(n). Then the dimension of the space of polynomial solutions of the equation p[u] = 0 on R-n must be infinite.

引用

页码：1148 / 1155

页数：8

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