[1]伍芸.含Hardy位势的双调和方程在R4中非平凡解问题[J].南京师大学报(自然科学版),2014,37(02):44.
　Wu Yun.Nontrivial Solution Problems of Biharmonic Equation with Hardy Potential in R4[J].Journal of Nanjing Normal University(Natural Science Edition),2014,37(02):44.
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含Hardy位势的双调和方程在R4中非平凡解问题()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第37卷
期数:
2014年02期
页码:
44
栏目:
数学
出版日期:
2014-06-30

文章信息/Info

Title:
Nontrivial Solution Problems of Biharmonic Equation with Hardy Potential in R4
作者:
伍芸
贵州师范大学数学与计算机科学学院,贵州 贵阳 550001
Author(s):
Wu Yun
School of Mathematics and Computer Science,Guizhou Normal University,Guiyang 550001,China
关键词:
特征值问题; 双调和; Hardy位势
Keywords:
eigenvalue problem; biharmonic; Hardy potential
分类号:
O175.25
文献标志码:
A
摘要:
本文考虑在R4中含Hardy位势1|x|4(lnR/|x|)2的双调和方程非平凡解问题.通过重新赋范的方法,将H20(Ω)赋范并按新的范数建立一个完备的、新的Hilbert空间H.并利用HardyRellich不等式,证明了此双调和方程在H中存在一个非平凡解.
Abstract:
This paper considers eigenvalue problems of a biharmonic equation with Hardy potential:1|x|4(lnR/|x|)2 in R4.By the way of renormed,we have a new Hilbert space H.Furthermore using the HardyRellich inequality,we prove that there is a nontrivial solution for these problems in a new space H.

参考文献/References:

[1]Adimurthi,Massimo Grossi,Sanjiban Santra.Optimal HardyRellich inequalities,maximum principle and related eigenvalue problem[J].Journal of Functional Analysis,2006,240:36-83.
[2]陈志辉,沈尧天,姚仰新.R4中含位势的非线性双调和方程[J].数学年刊,2005,26A(4):487-494.
[3]陈志辉,沈尧天.含距离位势的拟线性椭圆方程解的存在性[J].数学学报,2008,51(3):469-474.
[4]ZK Adams R A.Sobolev Spaces[M].Salt Lake City:Academic Press,1978.
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备注/Memo

备注/Memo:
收稿日期:2013-08-26.
基金项目:国家自然科学基金(10771074)、贵州省科学技术厅—贵州师范大学联合基金(黔科合J字LKS[2012]14号).
通讯联系人:伍芸,副教授,研究方向:非线性椭圆型方程.E-mail:wuyun73224@163.com
更新日期/Last Update: 2014-06-30