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一类四阶奇异微分算子的左定边界条件
  • ISSN号：1000-4424
  • 期刊名称：高校应用数学学报A辑(中文版)
  • 时间：2012.5.8
  • 页码：182-192
  • 分类：O175.3[理学—数学;理学—基础数学]
  • 作者机构：[1]内蒙古工业大学理学院数学系,内蒙古呼和浩特010051
  • 相关基金：国家自然科学基金（11171295）
  • 相关项目：非自伴微分算子谱理论及其应用
作者： 王琳|高云兰|刘雪英|
关键词： 四阶奇异微分算子, 左定边界条件, 边值矩阵, fourth-order singular differential operators, left-definite boundary conditions, bound- ary matrix
中文摘要：

利用左定微分算子与相应的右定微分算子之间的关系来研究左定微分算子.首先给出四阶奇异微分算子的自共轭域;接着利用主解与Friedrichs扩张寻找最小算子的正的自共轭扩张;最后通过系数、区间端点和边界条件给出四阶奇异微分算子左定性的充要条件以及相应的左定边值矩阵的情形.

英文摘要：

In this paper, a class of fourth-order singular differential operators is studied. The relationship between left-definite differential operators and the corresponding right-definite ones is used. Firstly, the self-adjoint domains of fourth-order singular differential operators are given. Secondly, positive self-adjoint extension of the minimal operator is obtained, in which the principal solution and Friedrichs expansion of the operators are used. Finally, the necessary and sufficient conditions of the operator＇s left-definiteness are got, which depend on the coefficients, the endpoints and the boundary conditions. Moreover, all the cases of the left-definite boundary matrix are given here.

同期刊论文项目
非自伴微分算子谱理论及其应用
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期刊信息
  • 《高校应用数学学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:浙江大学 中国工业与应用数学学会
  • 主编：林正炎 李大潜
  • 地址：杭州市玉泉浙江大学数学系
  • 邮编：310027
  • 邮箱：amjcu@zjy.edu.cn
  • 电话：0571-87951602
  • 国际标准刊号：ISSN：1000-4424
  • 国内统一刊号：ISSN：33-1110/O
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:3669