| 边界条件中含谱参数的Sturm-Liouville算子特征值的渐进式 |
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| 引用本文： | 马美绒.边界条件中含谱参数的Sturm-Liouville算子特征值的渐进式[J].宝鸡文理学院学报(自然科学版),2012,32(4):16-20. |
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| 作者姓名： | 马美绒 |
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| 作者单位： | 陕西师范大学数学与信息科学学院,陕西西安,710062 |
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| 基金项目： | 国家自然科学基金资助项目 |
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| 摘 要： | 目的研究边界条件中合谱参数的S—L（Sturm—Liouville）算子的特征值。方法利用微分方程的基本解的高阶展开式及其系数特征，采用剩余估计法。结果得到边界条件中合谱参数的S-L算子的特征值渐进式。结论改善了此类S-L问题的特征值的渐进性。
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| 关 键 词： | Sturm-Liouville算子 特征值 基本解 |
Asymptotic behavior for eigenvalues of Sturm-Liouville operators with boundary conditions containing spectral parameter |
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| MA Mei-rong.Asymptotic behavior for eigenvalues of Sturm-Liouville operators with boundary conditions containing spectral parameter[J].Journal of Baoji College of Arts and Science(Natural Science Edition),2012,32(4):16-20. |
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| Authors: | MA Mei-rong |
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| Institution: | MA Mei-rong(College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,Shaanxi,China) |
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| Abstract: | Aim To study the asymptotic behavior for eigenvalues of Sturm-Liouville operators with boundary conditions containing spectral parameter. Method The residual estimation method is adopted which is based on the high order expansion and coefficient feature of basic solution of differen- tial equation. Result The asymptotic expressions for eigenvalues of the Sturm-Liouville operators areobtained. Conclusion The asymptotic behavior for this S-L problem has been improved. |
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| Keywords: | Sturm-Liouville operator eigenvalue solution |
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