| Discontinuous Sturm-Liouville Problems Containing Eigenparameter in the Boundary Conditions |
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| 引用本文： | M. KADAKAL O. Sh. MUKHTAROV. Discontinuous Sturm-Liouville Problems Containing Eigenparameter in the Boundary Conditions[J]. 数学学报(英文版), 2006, 22(5): 1519-1528. DOI: 10.1007/s10114-005-0751-x |
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| 作者姓名： | M. KADAKAL O. Sh. MUKHTAROV |
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| 作者单位： | [1]Ondokuz Mayzs University, Science and Arts Faculty, Department of Mathematics, Kurupelit 55139, Samsun, Turkey [2]Gaziosmanpasa University, Science and Arts Faculty, Department of Mathematics, Tokat 60000, Turkey |
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| 摘 要： | In this paper, discontinuous Sturm-Liouville problems, which contain eigenvalue parameters both in the equation and in one of the boundary conditions, are investigated. By using an operatortheoretic interpretation we extend some classic results for regular Sturm-Liouville problems and obtain asymptotic approximate formulae for eigenvalues and normalized eigenfunctions. We modify some techniques of [Fulton, C. T., Proc. Roy. Soc. Edin. 77 （A）, 293-308 （1977）], [Walter, J., Math. Z., 133, 301-312 （1973）] and [Titchmarsh, E. C., Eigenfunctions Expansion Associated with Second Order Differential Equations I, 2nd edn., Oxford Univ. Pres, London, 1962], then by using these techniques we obtain asymptotic formulae for eigenelement norms and normalized eigenfunctions.
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| 关 键 词： | Sturm-Liouville问题 不连续边界值问题 特征值 本征函数 |
| 收稿时间： | 2004-08-12 |
| 修稿时间： | 2004-08-122004-12-13 |
Discontinuous Sturm–Liouville Problems Containing Eigenparameter in the Boundary Conditions |
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| M. Kadakal,O. Sh. Mukhtarov. Discontinuous Sturm–Liouville Problems Containing Eigenparameter in the Boundary Conditions[J]. Acta Mathematica Sinica(English Series), 2006, 22(5): 1519-1528. DOI: 10.1007/s10114-005-0751-x |
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| Authors: | M. Kadakal O. Sh. Mukhtarov |
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| Affiliation: | (1) Ondokuz Mayıs University, Science and Arts Faculty, Department of Mathematics, Kurupelit 55139, Samsun, Turkey;(2) Gaziosmanpaşa University, Science and Arts Faculty, Department of Mathematics, Tokat 60000, Turkey |
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| Abstract: | In this paper, discontinuous Sturm–Liouville problems, which contain eigenvalue parameters both in the equation and in one of the boundary conditions, are investigated. By using an operatortheoretic interpretation we extend some classic results for regular Sturm–Liouville problems and obtain asymptotic approximate formulae for eigenvalues and normalized eigenfunctions. We modify some techniques of [Fulton, C. T., Proc. Roy. Soc. Edin. 77 (A), 293–308 (1977)], [Walter, J., Math. Z., 133, 301–312 (1973)] and [Titchmarsh, E. C., Eigenfunctions Expansion Associated with Second Order Differential Equations I, 2nd edn., Oxford Univ. Pres, London, 1962], then by using these techniques we obtain asymptotic formulae for eigenelement norms and normalized eigenfunctions. |
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| Keywords: | Sturm-Liouville problem discontinuous boundary-value problem eigenvalue and eigenfunction eigenelement normalized eigenfunctions |
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