Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities
We study the existence of positive solutions for a fourth order semilinear elliptic equation under Navier boundary conditions with positive, increasing and convex source term. Both bounded and unbounded solutions are considered. When compared with second order equations, several differences and diff...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2005-03-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2005/34/abstr.html |
| _version_ | 1818251212384894976 |
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| author | Filippo Gazzola Elvise Berchio |
| author_facet | Filippo Gazzola Elvise Berchio |
| author_sort | Filippo Gazzola |
| collection | DOAJ |
| description | We study the existence of positive solutions for a fourth order semilinear elliptic equation under Navier boundary conditions with positive, increasing and convex source term. Both bounded and unbounded solutions are considered. When compared with second order equations, several differences and difficulties arise. In order to overcome these difficulties new ideas are needed. But still, in some cases we are able to extend only partially the well-known results for second order equations. The theoretical and numerical study of radial solutions in the ball also reveal some new phenomena, not available for second order equations. These phenomena suggest a number of intriguing unsolved problems, which we quote in the final section. |
| first_indexed | 2024-12-12T16:04:42Z |
| format | Article |
| id | doaj.art-3a1586b10b42407eb9501102d94fae93 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T16:04:42Z |
| publishDate | 2005-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-3a1586b10b42407eb9501102d94fae932022-12-22T00:19:20ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912005-03-01200534120Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearitiesFilippo GazzolaElvise BerchioWe study the existence of positive solutions for a fourth order semilinear elliptic equation under Navier boundary conditions with positive, increasing and convex source term. Both bounded and unbounded solutions are considered. When compared with second order equations, several differences and difficulties arise. In order to overcome these difficulties new ideas are needed. But still, in some cases we are able to extend only partially the well-known results for second order equations. The theoretical and numerical study of radial solutions in the ball also reveal some new phenomena, not available for second order equations. These phenomena suggest a number of intriguing unsolved problems, which we quote in the final section.http://ejde.math.txstate.edu/Volumes/2005/34/abstr.htmlSemilinear biharmonic equationsminimal solutionsextremal solutions. |
| spellingShingle | Filippo Gazzola Elvise Berchio Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities Electronic Journal of Differential Equations Semilinear biharmonic equations minimal solutions extremal solutions. |
| title | Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities |
| title_full | Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities |
| title_fullStr | Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities |
| title_full_unstemmed | Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities |
| title_short | Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities |
| title_sort | some remarks on biharmonic elliptic problems with positive increasing and convex nonlinearities |
| topic | Semilinear biharmonic equations minimal solutions extremal solutions. |
| url | http://ejde.math.txstate.edu/Volumes/2005/34/abstr.html |
| work_keys_str_mv | AT filippogazzola someremarksonbiharmonicellipticproblemswithpositiveincreasingandconvexnonlinearities AT elviseberchio someremarksonbiharmonicellipticproblemswithpositiveincreasingandconvexnonlinearities |