| 边界条件含特征参数的Sturm-Liouville问题的特征值比率 |
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| 引用本文： | 张茂柱,孙炯.边界条件含特征参数的Sturm-Liouville问题的特征值比率[J].数学的实践与认识,2011,41(17). |
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| 作者姓名： | 张茂柱 孙炯 |
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| 作者单位： | 1. 内蒙古大学数学科学学院,内蒙古呼和浩特010021;泰山学院数学与系统科学学院,山东泰安271021
2. 内蒙古大学数学科学学院,内蒙古呼和浩特,010021 |
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| 基金项目： | 国家自然科学基金(10861008) |
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| 摘 要： | 给出修正Prfer变换的几何意义以及相关性质,并利用上述性质讨论Sturm-Liouville问题-(py′)′+gy=λωy,x∈0,1],参数边界条件为y(0)=0与((py′)(1))/(y(1))=aλ+b,得到了当a>0,q≥0的特征值比率上界,这把Ashbaugh等人的结果推广到边界条件含参数的情形.
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| 关 键 词： | Sturm-Liouville问题 参数边界条件 特征值比率 |
Eigenvalue Ratios for Sturm-Liouville Problem with Eigenparameter in the Boundary Conditions |
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| ZHANG Mao-zhu,SUN Jiong.Eigenvalue Ratios for Sturm-Liouville Problem with Eigenparameter in the Boundary Conditions[J].Mathematics in Practice and Theory,2011,41(17). |
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| Authors: | ZHANG Mao-zhu SUN Jiong |
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| Institution: | ZHANG Mao-zhu~(1,2),SUN Jiong~1 (1.School of Mathematics Science,Inner Mongolia University,Hohhot 010021,China) (2.College of Mathematics and System Science,Taishan University,Taian,Shandong 271021,China) |
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| Abstract: | The geometric aspect of modified Prfer transformation and related properties are given in this paper.Using the above,we consider Sturm-Liouville problem -(py')' + qy =λωy with boundary conditions y(0) = 0 and(py')(1)/y(1)=αλ+b,where a>0.We obtain eigenvalue ratios of the above problem when q≥0,which extends Ashbaugh's result to Sturm-Liouville problems with eigenparameter in the boundary conditions. |
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| Keywords: | Sturm-Liouville problem Eigenparameter dependent boundary conditions Eigenvalue ratios |
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