On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value
This study concerns the existence of positive solutions to classes of boundary value problems of the form −∆u = g(x,u), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (se...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2006-11-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | http://www.journals.vu.lt/nonlinear-analysis/article/view/14736 |
| _version_ | 1818384631998709760 |
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| author | G. A. Afrouzi S. H. Rasouli |
| author_facet | G. A. Afrouzi S. H. Rasouli |
| author_sort | G. A. Afrouzi |
| collection | DOAJ |
| description | This study concerns the existence of positive solutions to classes of boundary value problems of the form
−∆u = g(x,u), x ∈ Ω,
u(x) = 0, x ∈ ∂Ω,
where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u). |
| first_indexed | 2024-12-14T03:25:20Z |
| format | Article |
| id | doaj.art-e0bcba9a18074cdcbd6c6397d3ad8b34 |
| institution | Directory Open Access Journal |
| issn | 1392-5113 2335-8963 |
| language | English |
| last_indexed | 2024-12-14T03:25:20Z |
| publishDate | 2006-11-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj.art-e0bcba9a18074cdcbd6c6397d3ad8b342022-12-21T23:18:53ZengVilnius University PressNonlinear Analysis1392-51132335-89632006-11-0111410.15388/NA.2006.11.4.14736On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary ValueG. A. Afrouzi0S. H. Rasouli1Mazandaran University, IranMazandaran University, IranThis study concerns the existence of positive solutions to classes of boundary value problems of the form −∆u = g(x,u), x ∈ Ω, u(x) = 0, x ∈ ∂Ω, where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u).http://www.journals.vu.lt/nonlinear-analysis/article/view/14736positive solutionssub-super solution |
| spellingShingle | G. A. Afrouzi S. H. Rasouli On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value Nonlinear Analysis positive solutions sub-super solution |
| title | On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value |
| title_full | On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value |
| title_fullStr | On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value |
| title_full_unstemmed | On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value |
| title_short | On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value |
| title_sort | on positive solutions for some nonlinear semipositone elliptic boundary value |
| topic | positive solutions sub-super solution |
| url | http://www.journals.vu.lt/nonlinear-analysis/article/view/14736 |
| work_keys_str_mv | AT gaafrouzi onpositivesolutionsforsomenonlinearsemipositoneellipticboundaryvalue AT shrasouli onpositivesolutionsforsomenonlinearsemipositoneellipticboundaryvalue |