Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients
This paper gives sufficient and necessary conditions for the classification of Sturm-Liouville differential equations with complex coefficients given by Brown et al. These conditions involve weighted Sobolev subspaces and the asymptotic behavior of elements in the maximal domain. The results of the...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/340796 |
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| _version_ | 1850215095444963328 |
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| author | Bing Xie Jian Gang Qi |
| author_facet | Bing Xie Jian Gang Qi |
| author_sort | Bing Xie |
| collection | DOAJ |
| description | This paper gives sufficient and necessary conditions for the classification of Sturm-Liouville differential equations with complex coefficients given by Brown et al. These conditions involve weighted Sobolev subspaces and the asymptotic behavior of elements in the maximal domain. The results of the present paper generalize the corresponding results for formally symmetric Sturm-Liouville differential equations to non-self-adjoint cases. |
| format | Article |
| id | doaj-art-7f9fb606221047aeaa949324cdf6dd46 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-7f9fb606221047aeaa949324cdf6dd462025-08-20T02:08:43ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/340796340796Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex CoefficientsBing Xie0Jian Gang Qi1Department of Mathematics, Shandong University at Weihai, Weihai 264209, ChinaDepartment of Mathematics, Shandong University at Weihai, Weihai 264209, ChinaThis paper gives sufficient and necessary conditions for the classification of Sturm-Liouville differential equations with complex coefficients given by Brown et al. These conditions involve weighted Sobolev subspaces and the asymptotic behavior of elements in the maximal domain. The results of the present paper generalize the corresponding results for formally symmetric Sturm-Liouville differential equations to non-self-adjoint cases.http://dx.doi.org/10.1155/2011/340796 |
| spellingShingle | Bing Xie Jian Gang Qi Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients Abstract and Applied Analysis |
| title | Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients |
| title_full | Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients |
| title_fullStr | Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients |
| title_full_unstemmed | Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients |
| title_short | Sufficient and Necessary Conditions for the Classification of Sturm-Liouville Differential Equations with Complex Coefficients |
| title_sort | sufficient and necessary conditions for the classification of sturm liouville differential equations with complex coefficients |
| url | http://dx.doi.org/10.1155/2011/340796 |
| work_keys_str_mv | AT bingxie sufficientandnecessaryconditionsfortheclassificationofsturmliouvilledifferentialequationswithcomplexcoefficients AT jiangangqi sufficientandnecessaryconditionsfortheclassificationofsturmliouvilledifferentialequationswithcomplexcoefficients |