Dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition
In this paper, we discuss the continuous dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition by using of implicit function theorem. A geometric structure on SL(2,R) containing real coupled boundary conditions is firstly clarified, that is, the smooth embeddin...
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| Veröffentlicht in: | Journal of mathematical analysis and applications Jg. 538; H. 2; S. 128398 |
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| Sprache: | Englisch |
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| Abstract | In this paper, we discuss the continuous dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition by using of implicit function theorem. A geometric structure on SL(2,R) containing real coupled boundary conditions is firstly clarified, that is, the smooth embedding submanifold. Under this structure, we verify the continuous differentiability of the n-th eigenvalue with regard to the boundary condition and explicitly present the expression for its differential. Moreover, a sufficient condition for recognizing double eigenvalues is given. |
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| AbstractList | In this paper, we discuss the continuous dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition by using of implicit function theorem. A geometric structure on SL(2,R) containing real coupled boundary conditions is firstly clarified, that is, the smooth embedding submanifold. Under this structure, we verify the continuous differentiability of the n-th eigenvalue with regard to the boundary condition and explicitly present the expression for its differential. Moreover, a sufficient condition for recognizing double eigenvalues is given. |
| ArticleNumber | 128398 |
| Author | Yang, Xinya |
| Author_xml | – sequence: 1 givenname: Xinya orcidid: 0009-0005-1359-6792 surname: Yang fullname: Yang, Xinya email: yangxinyacn@163.com organization: Shanxi Engineering Vocational College, Taiyuan 030009, PR China |
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| Cites_doi | 10.1016/j.jde.2015.12.027 10.1002/cpa.3160360604 10.1006/jdeq.1996.0056 10.1002/mma.9142 10.1002/cpa.3160370205 10.1017/S0308210500000305 10.1002/cpa.3160370102 10.1002/mana.19971880111 10.1006/jdeq.1996.0154 10.1090/S0002-9947-03-03028-9 10.1017/S0308210500022885 10.1007/978-1-4757-2201-7 |
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| Keywords | Implicit function theorem Real coupled boundary condition Smooth manifold Differential |
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| Title | Dependence of eigenvalue of Sturm-Liouville operators on the real coupled boundary condition |
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