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超线性Fredholm积分方程的非平凡解及其应用
  • ISSN号：1003-3998
  • 期刊名称：数学物理学报
  • 时间：0
  • 页码：1230-1238
  • 分类：O175.14[理学—数学;理学—基础数学]
  • 作者机构：[1]江西财经大学数学系,南昌330013
  • 相关基金：国家自然科学基金（11161022,10701040,60964005）、江西省自然科学基金（2009GQS0007）和江西省教育厅科技项目（GJJ11420）资助
  • 相关项目：基于非线性特征辨识的高炉炉温混合控制模型研究
作者： 李志龙|
关键词： 拓扑度, FREDHOLM积分方程, 非平凡解, 下方无界, Topological degree, Fredholm integral equations, Nontrivial solutions, Unbounded below.
中文摘要：

利用拓扑度计算，在非线性项可变号且下方无界的情形下，得到了一个超线Predholm积分方程的非平凡解存在性定理．同时将其应用到Sturm—Liouville问题的解的存在性问题研究，其中系数函数q（t）允许在t=0，1处奇异．

英文摘要：

By computation of topological degree the author establishes an existence theorem on nontrivial solutions for superlinear Fredholm integral equations in which the nonlinearity is allowed to be sign-changed and unbounded below. Applying it, the author discusses the existence of solutions of Sturm-Liouville problems in which the coefficient function q（t） is admitted to be singular at t =0, 1.

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期刊信息
  • 《数学物理学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:中国科学院
  • 主办单位:中国科学院武汉物理与数学研究所
  • 主编：李邦河 陈贵强 朱熹平
  • 地址：湖北省武汉市武昌小洪山西路30号武汉71010信箱
  • 邮编：430071
  • 邮箱：actams@wipm.ac.cn
  • 电话：027-87199206
  • 国际标准刊号：ISSN：1003-3998
  • 国内统一刊号：ISSN：42-1226/O
  • 邮发代号:38-214
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,日本日本科学技术振兴机构数据库,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:5382