Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities
We study the exact number of positive solutions of a two-point Dirichlet boundary-value problem involving the p-Laplacian operator. We consider the case $p=2$ and the case $p>1$, when the nonlinearity satisfies $f(0)>0$ (positone) and has three distinct simple positive zeros and such that $f&#...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2004-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/72/abstr.html |
| _version_ | 1818787058730139648 |
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| author | Idris Addou Shin-Hwa Wang |
| author_facet | Idris Addou Shin-Hwa Wang |
| author_sort | Idris Addou |
| collection | DOAJ |
| description | We study the exact number of positive solutions of a two-point Dirichlet boundary-value problem involving the p-Laplacian operator. We consider the case $p=2$ and the case $p>1$, when the nonlinearity satisfies $f(0)>0$ (positone) and has three distinct simple positive zeros and such that $f''$ changes sign exactly twice on $(0,infty)$. Note that we may allow $f''$ to change sign more than twice on $(0,infty )$. We also present some interesting examples. |
| first_indexed | 2024-12-18T14:01:44Z |
| format | Article |
| id | doaj.art-23d492e6976c453e9dedb5db0fb378ff |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-18T14:01:44Z |
| publishDate | 2004-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-23d492e6976c453e9dedb5db0fb378ff2022-12-21T21:05:18ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-05-01200472124Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearitiesIdris AddouShin-Hwa WangWe study the exact number of positive solutions of a two-point Dirichlet boundary-value problem involving the p-Laplacian operator. We consider the case $p=2$ and the case $p>1$, when the nonlinearity satisfies $f(0)>0$ (positone) and has three distinct simple positive zeros and such that $f''$ changes sign exactly twice on $(0,infty)$. Note that we may allow $f''$ to change sign more than twice on $(0,infty )$. We also present some interesting examples.http://ejde.math.txstate.edu/Volumes/2004/72/abstr.htmlExact multiplicity resultp-Laplacianpositone problembifurcationconcave-convex-concave nonlinearity |
| spellingShingle | Idris Addou Shin-Hwa Wang Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities Electronic Journal of Differential Equations Exact multiplicity result p-Laplacian positone problem bifurcation concave-convex-concave nonlinearity |
| title | Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities |
| title_full | Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities |
| title_fullStr | Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities |
| title_full_unstemmed | Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities |
| title_short | Exact multiplicity results for a p-Laplacian positone problem with concave-convex-concave nonlinearities |
| title_sort | exact multiplicity results for a p laplacian positone problem with concave convex concave nonlinearities |
| topic | Exact multiplicity result p-Laplacian positone problem bifurcation concave-convex-concave nonlinearity |
| url | http://ejde.math.txstate.edu/Volumes/2004/72/abstr.html |
| work_keys_str_mv | AT idrisaddou exactmultiplicityresultsforaplaplacianpositoneproblemwithconcaveconvexconcavenonlinearities AT shinhwawang exactmultiplicityresultsforaplaplacianpositoneproblemwithconcaveconvexconcavenonlinearities |