A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence
The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution e...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/5/658 |
| _version_ | 1797569584899817472 |
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| author | Dumitru Motreanu Angela Sciammetta Elisabetta Tornatore |
| author_facet | Dumitru Motreanu Angela Sciammetta Elisabetta Tornatore |
| author_sort | Dumitru Motreanu |
| collection | DOAJ |
| description | The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions. |
| first_indexed | 2024-03-10T20:12:39Z |
| format | Article |
| id | doaj.art-a011835d00674bdda05bed516b703118 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T20:12:39Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-a011835d00674bdda05bed516b7031182023-11-19T22:49:10ZengMDPI AGMathematics2227-73902020-04-018565810.3390/math8050658A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient DependenceDumitru Motreanu0Angela Sciammetta1Elisabetta Tornatore2Department of Mathematics, University of Perpignan, 66860 Perpignan, FranceDepartment of Mathematics and Computer Science, University of Palermo, 90123 Palermo, ItalyDepartment of Mathematics and Computer Science, University of Palermo, 90123 Palermo, ItalyThe paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems. The main result establishes the existence of a solution enclosed in the ordered interval formed by a sub-supersolution. The result is applied to find positive solutions.https://www.mdpi.com/2227-7390/8/5/658nonlinear elliptic problemRobin boundary conditiongradient dependencesub-supersolutionpositive solution |
| spellingShingle | Dumitru Motreanu Angela Sciammetta Elisabetta Tornatore A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence Mathematics nonlinear elliptic problem Robin boundary condition gradient dependence sub-supersolution positive solution |
| title | A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence |
| title_full | A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence |
| title_fullStr | A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence |
| title_full_unstemmed | A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence |
| title_short | A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence |
| title_sort | sub supersolution approach for robin boundary value problems with full gradient dependence |
| topic | nonlinear elliptic problem Robin boundary condition gradient dependence sub-supersolution positive solution |
| url | https://www.mdpi.com/2227-7390/8/5/658 |
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