Polynomial solutions of quasi-homogeneous partial differential equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Polynomial solutions of quasi-homogeneous partial differential equations

Authors:	Luo Xuebo ZHENG Zhujun

Affiliation:	1. Institute of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China; 2. Institute of Mathematics, Henan University, Kaifeng 475001, China

Abstract:	By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation $left{ {delta _tau } right}{text{ }}_{tau< 0}$ given by ( a₁, …, a_n). Assume that either a₁, …, a_n are positive rational numbers or $m{text{ = }}sumlimits_{j = 1}^n {alpha _j alpha _j }$ for some $alpha {text{ = }}left( {alpha _1 ,{text{ }} ldots {text{ }},alpha _n } right) in l _ + ^n$ Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝⁿ must be infinite

Keywords:	quasi-homogeneous partial differential operator polynomial solution, dimension of the space of solution method of analytic number theory
本文献已被万方数据 SpringerLink 等数据库收录！