On the Neumann eigenvalues for second-order Sturm–Liouville difference equations
Abstract The paper is concerned with the Neumann eigenvalues for second-order Sturm–Liouville difference equations. By analyzing the new discriminant function, we show the interlacing properties between the periodic, antiperiodic, and Neumann eigenvalues. Moreover, when the potential sequence is sym...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03064-3 |
| _version_ | 1818301953105461248 |
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| author | Yan-Hsiou Cheng |
| author_facet | Yan-Hsiou Cheng |
| author_sort | Yan-Hsiou Cheng |
| collection | DOAJ |
| description | Abstract The paper is concerned with the Neumann eigenvalues for second-order Sturm–Liouville difference equations. By analyzing the new discriminant function, we show the interlacing properties between the periodic, antiperiodic, and Neumann eigenvalues. Moreover, when the potential sequence is symmetric and symmetric monotonic, we show the order relation between the first Dirichlet eigenvalue and the second Neumann eigenvalue, and prove that the minimum of the first Neumann eigenvalue gap is attained at the constant potential sequence. |
| first_indexed | 2024-12-13T05:31:12Z |
| format | Article |
| id | doaj.art-33521a91bcd5477fbd3f583de077307b |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-13T05:31:12Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-33521a91bcd5477fbd3f583de077307b2022-12-21T23:58:04ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020111710.1186/s13662-020-03064-3On the Neumann eigenvalues for second-order Sturm–Liouville difference equationsYan-Hsiou Cheng0Department of Mathematics and Information Education, National Taipei University of EducationAbstract The paper is concerned with the Neumann eigenvalues for second-order Sturm–Liouville difference equations. By analyzing the new discriminant function, we show the interlacing properties between the periodic, antiperiodic, and Neumann eigenvalues. Moreover, when the potential sequence is symmetric and symmetric monotonic, we show the order relation between the first Dirichlet eigenvalue and the second Neumann eigenvalue, and prove that the minimum of the first Neumann eigenvalue gap is attained at the constant potential sequence.http://link.springer.com/article/10.1186/s13662-020-03064-3Second-order difference equationsEigenvalue gapNeumann eigenvalues |
| spellingShingle | Yan-Hsiou Cheng On the Neumann eigenvalues for second-order Sturm–Liouville difference equations Advances in Difference Equations Second-order difference equations Eigenvalue gap Neumann eigenvalues |
| title | On the Neumann eigenvalues for second-order Sturm–Liouville difference equations |
| title_full | On the Neumann eigenvalues for second-order Sturm–Liouville difference equations |
| title_fullStr | On the Neumann eigenvalues for second-order Sturm–Liouville difference equations |
| title_full_unstemmed | On the Neumann eigenvalues for second-order Sturm–Liouville difference equations |
| title_short | On the Neumann eigenvalues for second-order Sturm–Liouville difference equations |
| title_sort | on the neumann eigenvalues for second order sturm liouville difference equations |
| topic | Second-order difference equations Eigenvalue gap Neumann eigenvalues |
| url | http://link.springer.com/article/10.1186/s13662-020-03064-3 |
| work_keys_str_mv | AT yanhsioucheng ontheneumanneigenvaluesforsecondordersturmliouvilledifferenceequations |