姚庆六.具有正Green函数的奇异Sturm-Liouville边值问题的正解[J].数学研究及应用,2013,33(5):561~568
具有正Green函数的奇异Sturm-Liouville边值问题的正解
Positive Solutions of Singular Sturm-Liouville Boundary Value Problems with Positive Green Function
投稿时间:2012-05-24  最后修改时间:2012-09-03
DOI:10.3770/j.issn:2095-2651.2013.05.005
中文关键词:  奇异常微分方程  Sturm-Liouville边值问题  正解  存在性与多解性.
英文关键词:singular ordinary differential equation  Sturm-Liouville boundary value problem  positive solution  existence and multiplicity.
基金项目:国家自然科学基金(Grant No.11071109).
作者单位
姚庆六 南京财经大学应用数学系, 江苏 南京 210003 
摘要点击次数: 1341
全文下载次数: 1358
中文摘要:
      考察了具有正Green函数的奇异Sturm-Liouville边值问题的正解存在性与多解性,其中相对于空间变元非线性项可以是超强奇异的.通过构造适当的控制函数,精确估计了解的先验界.利用锥压缩-拉伸型的Guo-Krasnosel'skii不动点定理,证明了几个存在结论.
英文摘要:
      The existence and multiplicity of positive solutions are studied for a singular Sturm-Liouville boundary value problem with positive Green function, where the nonlinearity may be super-strongly singular with respect to the space variable. By constructing suitable control functions, the a priori bound of solution is exactly estimated. By applying the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several existence results are proved.
查看全文  查看/发表评论  下载PDF阅读器