Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k)
A delayed discrete equation Δu(k+n)=−p(k)u(k) with positive coefficient p is considered. Sufficient conditions with respect to p are formulated in order to guarantee the existence of positive solutions if k→∞. As a tool of the proof of corresponding result, the method described in the author's...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337504306056 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832564237878165504 |
|---|---|
| author | Jaromír Baštinec Josef Diblík |
| author_facet | Jaromír Baštinec Josef Diblík |
| author_sort | Jaromír Baštinec |
| collection | DOAJ |
| description | A delayed discrete equation Δu(k+n)=−p(k)u(k) with positive coefficient p is considered. Sufficient conditions with respect to p are formulated in order to guarantee the existence of positive solutions if k→∞. As a tool of the proof of corresponding result, the method described in the author's previous papers is used. Except for the fact of the existence of positive solutions, their upper estimation is given. The analysis shows that every positive solution of the indicated family of positive solutions tends to zero (if k→∞) with the speednot smaller than the speed characterized by the function k·(n/(n+1))k. A comparison with the known results is given and some open questions are discussed. |
| format | Article |
| id | doaj-art-06c9cf0b7b1f434c8776d555a3e2dfb2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-06c9cf0b7b1f434c8776d555a3e2dfb22025-02-03T01:11:22ZengWileyAbstract and Applied Analysis1085-33751687-04092004-01-012004646147010.1155/S1085337504306056Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k)Jaromír Baštinec0Josef Diblík1Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technick 8, Brno 616 00, Czech RepublicDepartment of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Žižkova 17, Brno 662 37, Czech RepublicA delayed discrete equation Δu(k+n)=−p(k)u(k) with positive coefficient p is considered. Sufficient conditions with respect to p are formulated in order to guarantee the existence of positive solutions if k→∞. As a tool of the proof of corresponding result, the method described in the author's previous papers is used. Except for the fact of the existence of positive solutions, their upper estimation is given. The analysis shows that every positive solution of the indicated family of positive solutions tends to zero (if k→∞) with the speednot smaller than the speed characterized by the function k·(n/(n+1))k. A comparison with the known results is given and some open questions are discussed.http://dx.doi.org/10.1155/S1085337504306056 |
| spellingShingle | Jaromír Baštinec Josef Diblík Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k) Abstract and Applied Analysis |
| title | Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k) |
| title_full | Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k) |
| title_fullStr | Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k) |
| title_full_unstemmed | Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k) |
| title_short | Subdominant positive solutions of the discrete equation Δu(k+n)=−p(k)u(k) |
| title_sort | subdominant positive solutions of the discrete equation δu k n p k u k |
| url | http://dx.doi.org/10.1155/S1085337504306056 |
| work_keys_str_mv | AT jaromirbastinec subdominantpositivesolutionsofthediscreteequationduknpkuk AT josefdiblik subdominantpositivesolutionsofthediscreteequationduknpkuk |