A focal boundary value problem for difference equations
The eigenvalue problem in difference equations, (−1)n−kΔny(t)=λ∑i=0k−1pi(t)Δiy(t), with Δty(0)=0, 0≤i≤k, Δk+iy(T+1)=0, 0≤i<n−k, is examined. Under suitable conditions on the coefficients pi, it is shown that the smallest positive eigenvalue is a decreasing function of T. As a consequence, results...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000201 |
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| _version_ | 1832546531948888064 |
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| author | Cathryn Denny Darrel Hankerson |
| author_facet | Cathryn Denny Darrel Hankerson |
| author_sort | Cathryn Denny |
| collection | DOAJ |
| description | The eigenvalue problem in difference equations, (−1)n−kΔny(t)=λ∑i=0k−1pi(t)Δiy(t),
with Δty(0)=0, 0≤i≤k, Δk+iy(T+1)=0, 0≤i<n−k, is examined. Under suitable conditions
on the coefficients pi, it is shown that the smallest positive eigenvalue is a decreasing function of
T. As a consequence, results concerning the first focal point for the boundary value problem with
λ=1 are obtained. |
| format | Article |
| id | doaj-art-690491d46a6a47b5896853903a38fd61 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1993-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-690491d46a6a47b5896853903a38fd612025-02-03T06:48:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116116917610.1155/S0161171293000201A focal boundary value problem for difference equationsCathryn Denny0Darrel Hankerson1Department of Algebra, Combinatorics, and Analysis, Auburn University, Auburn 36849-5307, Alabama, USADepartment of Algebra, Combinatorics, and Analysis, Auburn University, Auburn 36849-5307, Alabama, USAThe eigenvalue problem in difference equations, (−1)n−kΔny(t)=λ∑i=0k−1pi(t)Δiy(t), with Δty(0)=0, 0≤i≤k, Δk+iy(T+1)=0, 0≤i<n−k, is examined. Under suitable conditions on the coefficients pi, it is shown that the smallest positive eigenvalue is a decreasing function of T. As a consequence, results concerning the first focal point for the boundary value problem with λ=1 are obtained.http://dx.doi.org/10.1155/S0161171293000201difference equationeigenvalueboundary value problemfocal pointGreen's function. |
| spellingShingle | Cathryn Denny Darrel Hankerson A focal boundary value problem for difference equations International Journal of Mathematics and Mathematical Sciences difference equation eigenvalue boundary value problem focal point Green's function. |
| title | A focal boundary value problem for difference equations |
| title_full | A focal boundary value problem for difference equations |
| title_fullStr | A focal boundary value problem for difference equations |
| title_full_unstemmed | A focal boundary value problem for difference equations |
| title_short | A focal boundary value problem for difference equations |
| title_sort | focal boundary value problem for difference equations |
| topic | difference equation eigenvalue boundary value problem focal point Green's function. |
| url | http://dx.doi.org/10.1155/S0161171293000201 |
| work_keys_str_mv | AT cathryndenny afocalboundaryvalueproblemfordifferenceequations AT darrelhankerson afocalboundaryvalueproblemfordifferenceequations AT cathryndenny focalboundaryvalueproblemfordifferenceequations AT darrelhankerson focalboundaryvalueproblemfordifferenceequations |