Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem
A p-Laplacian boundary-value problem with positive nonlinearity is considered. The existence of a continuum of positive solutions emanating from $(lambda,u)=(0,0)$ is shown, and it can be extended to $lambda=infty$. Under an additional condition on the nonlinearity, it is shown that the positive...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2012-06-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2012/106/abstr.html |
| _version_ | 1819182034422071296 |
|---|---|
| author | Chan-Gyun Kim Junping Shi |
| author_facet | Chan-Gyun Kim Junping Shi |
| author_sort | Chan-Gyun Kim |
| collection | DOAJ |
| description | A p-Laplacian boundary-value problem with positive nonlinearity is considered. The existence of a continuum of positive solutions emanating from $(lambda,u)=(0,0)$ is shown, and it can be extended to $lambda=infty$. Under an additional condition on the nonlinearity, it is shown that the positive solution is unique for any $lambda>0$; thus the continuum $mathcal{C}$ is indeed a continuous curve globally defined for all $lambda>0$. In addition, by the upper and lower solutions method, existence of three positive solutions is established under some conditions on the nonlinearity. |
| first_indexed | 2024-12-22T22:39:43Z |
| format | Article |
| id | doaj.art-cbfdf80ecc5540beb983dc81cc7d5698 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-22T22:39:43Z |
| publishDate | 2012-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-cbfdf80ecc5540beb983dc81cc7d56982022-12-21T18:10:13ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912012-06-012012106,112Global continuum and multiple positive solutions to a p-Laplacian boundary-value problemChan-Gyun KimJunping ShiA p-Laplacian boundary-value problem with positive nonlinearity is considered. The existence of a continuum of positive solutions emanating from $(lambda,u)=(0,0)$ is shown, and it can be extended to $lambda=infty$. Under an additional condition on the nonlinearity, it is shown that the positive solution is unique for any $lambda>0$; thus the continuum $mathcal{C}$ is indeed a continuous curve globally defined for all $lambda>0$. In addition, by the upper and lower solutions method, existence of three positive solutions is established under some conditions on the nonlinearity.http://ejde.math.txstate.edu/Volumes/2012/106/abstr.htmlUpper and lower solutionpositive solutionp-Laplacianuniquenessmultiplicity |
| spellingShingle | Chan-Gyun Kim Junping Shi Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem Electronic Journal of Differential Equations Upper and lower solution positive solution p-Laplacian uniqueness multiplicity |
| title | Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem |
| title_full | Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem |
| title_fullStr | Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem |
| title_full_unstemmed | Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem |
| title_short | Global continuum and multiple positive solutions to a p-Laplacian boundary-value problem |
| title_sort | global continuum and multiple positive solutions to a p laplacian boundary value problem |
| topic | Upper and lower solution positive solution p-Laplacian uniqueness multiplicity |
| url | http://ejde.math.txstate.edu/Volumes/2012/106/abstr.html |
| work_keys_str_mv | AT changyunkim globalcontinuumandmultiplepositivesolutionstoaplaplacianboundaryvalueproblem AT junpingshi globalcontinuumandmultiplepositivesolutionstoaplaplacianboundaryvalueproblem |