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 |
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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 |
| Summary: | 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). |
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| ISSN: | 1392-5113 2335-8963 |