A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian
We introduce a reduction method for proving the existence of solutions to elliptic equations involving the p-Laplacian operator. The existence of solutions is implied by the existence of a positive essentially weak subsolution on a manifold and the existence of a positive supersolution on each compa...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2003-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2003/106/abstr.html |
| _version_ | 1818564327259504640 |
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| author | Mohamed Benalili Youssef Maliki |
| author_facet | Mohamed Benalili Youssef Maliki |
| author_sort | Mohamed Benalili |
| collection | DOAJ |
| description | We introduce a reduction method for proving the existence of solutions to elliptic equations involving the p-Laplacian operator. The existence of solutions is implied by the existence of a positive essentially weak subsolution on a manifold and the existence of a positive supersolution on each compact domain of this manifold. The existence and nonexistence of positive supersolutions is given by the sign of the first eigenvalue of a nonlinear operator. |
| first_indexed | 2024-12-14T01:27:35Z |
| format | Article |
| id | doaj.art-22bfc4eb444f4e7a99bacc0dd6ac40fd |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-14T01:27:35Z |
| publishDate | 2003-10-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-22bfc4eb444f4e7a99bacc0dd6ac40fd2022-12-21T23:22:08ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912003-10-012003106110A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacianMohamed BenaliliYoussef MalikiWe introduce a reduction method for proving the existence of solutions to elliptic equations involving the p-Laplacian operator. The existence of solutions is implied by the existence of a positive essentially weak subsolution on a manifold and the existence of a positive supersolution on each compact domain of this manifold. The existence and nonexistence of positive supersolutions is given by the sign of the first eigenvalue of a nonlinear operator.http://ejde.math.txstate.edu/Volumes/2003/106/abstr.htmlAnalysis on manifoldssemi-linear elliptic PDE. |
| spellingShingle | Mohamed Benalili Youssef Maliki A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian Electronic Journal of Differential Equations Analysis on manifolds semi-linear elliptic PDE. |
| title | A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian |
| title_full | A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian |
| title_fullStr | A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian |
| title_full_unstemmed | A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian |
| title_short | A reduction method for proving the existence of solutions to elliptic equations involving the p-laplacian |
| title_sort | reduction method for proving the existence of solutions to elliptic equations involving the p laplacian |
| topic | Analysis on manifolds semi-linear elliptic PDE. |
| url | http://ejde.math.txstate.edu/Volumes/2003/106/abstr.html |
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