Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type
In this work, we establish the existence of two intervals for a parameter $lambda$ for which a two-point boundary-value problem of fourth-order Sturm-Liouville type admits three weak solutions whose norms are uniformly bounded with respect to $lambda$. Employing two three critical point theorems...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-05-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/84/abstr.html |
| _version_ | 1811246362778402816 |
|---|---|
| author | Shapour Heidarkhani |
| author_facet | Shapour Heidarkhani |
| author_sort | Shapour Heidarkhani |
| collection | DOAJ |
| description | In this work, we establish the existence of two intervals for a parameter $lambda$ for which a two-point boundary-value problem of fourth-order Sturm-Liouville type admits three weak solutions whose norms are uniformly bounded with respect to $lambda$. Employing two three critical point theorems, existence of at least three weak solutions is ensured. This approach is based on variational methods and critical point theory. |
| first_indexed | 2024-04-12T14:52:24Z |
| format | Article |
| id | doaj.art-410e3801bfa846a6aa96489091433ce9 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T14:52:24Z |
| publishDate | 2012-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-410e3801bfa846a6aa96489091433ce92022-12-22T03:28:22ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-05-01201284,115Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville typeShapour HeidarkhaniIn this work, we establish the existence of two intervals for a parameter $lambda$ for which a two-point boundary-value problem of fourth-order Sturm-Liouville type admits three weak solutions whose norms are uniformly bounded with respect to $lambda$. Employing two three critical point theorems, existence of at least three weak solutions is ensured. This approach is based on variational methods and critical point theory.http://ejde.math.txstate.edu/Volumes/2012/84/abstr.htmlFourth-order Sturm-Liouville problemcritical pointmultiplicity of solutions |
| spellingShingle | Shapour Heidarkhani Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type Electronic Journal of Differential Equations Fourth-order Sturm-Liouville problem critical point multiplicity of solutions |
| title | Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type |
| title_full | Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type |
| title_fullStr | Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type |
| title_full_unstemmed | Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type |
| title_short | Existence of solutions for a two-point boundary-value problem of a fourth-order Sturm-Liouville type |
| title_sort | existence of solutions for a two point boundary value problem of a fourth order sturm liouville type |
| topic | Fourth-order Sturm-Liouville problem critical point multiplicity of solutions |
| url | http://ejde.math.txstate.edu/Volumes/2012/84/abstr.html |
| work_keys_str_mv | AT shapourheidarkhani existenceofsolutionsforatwopointboundaryvalueproblemofafourthordersturmliouvilletype |