On the existence of positive solutions for an ecological model with indefinite weight
This study concerns the existence of positive solutions for the following nonlinear boundary value problem: {−Δu=am(x)u−bu2−cupup+1−Kin Ω,u=0on ∂Ω, where Δu=div(∇u) is the Laplacian of u, while a,b,c,p,K are positive constants with p≥2 and Ω is a bounded smooth domain of RN with ∂Ω in C2. The weig...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2016-01-01
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| Series: | Arab Journal of Mathematical Sciences |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1319516615000067 |
| _version_ | 1819025507326361600 |
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| author | Saleh Shakeri Ghasem A. Afrouzi Armin Hadjian |
| author_facet | Saleh Shakeri Ghasem A. Afrouzi Armin Hadjian |
| author_sort | Saleh Shakeri |
| collection | DOAJ |
| description | This study concerns the existence of positive solutions for the following nonlinear boundary value problem: {−Δu=am(x)u−bu2−cupup+1−Kin Ω,u=0on ∂Ω, where Δu=div(∇u) is the Laplacian of u, while a,b,c,p,K are positive constants with p≥2 and Ω is a bounded smooth domain of RN with ∂Ω in C2. The weight function m satisfies m∈C(Ω) and m(x)≥m0>0 for x∈Ω, also ‖m‖∞=l<∞. We prove the existence of positive solutions under certain conditions. |
| first_indexed | 2024-12-21T05:11:47Z |
| format | Article |
| id | doaj.art-55b2d5a0d7f74eaaa78f0751b9da17af |
| institution | Directory Open Access Journal |
| issn | 1319-5166 |
| language | English |
| last_indexed | 2024-12-21T05:11:47Z |
| publishDate | 2016-01-01 |
| publisher | Emerald Publishing |
| record_format | Article |
| series | Arab Journal of Mathematical Sciences |
| spelling | doaj.art-55b2d5a0d7f74eaaa78f0751b9da17af2022-12-21T19:15:02ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662016-01-0122113213710.1016/j.ajmsc.2014.12.002On the existence of positive solutions for an ecological model with indefinite weightSaleh Shakeri0Ghasem A. Afrouzi1Armin Hadjian2Department of Mathematics, Islamic Azad University-Ayatollah Amoli Branch, Amol, IranDepartment of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranDepartment of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, IranThis study concerns the existence of positive solutions for the following nonlinear boundary value problem: {−Δu=am(x)u−bu2−cupup+1−Kin Ω,u=0on ∂Ω, where Δu=div(∇u) is the Laplacian of u, while a,b,c,p,K are positive constants with p≥2 and Ω is a bounded smooth domain of RN with ∂Ω in C2. The weight function m satisfies m∈C(Ω) and m(x)≥m0>0 for x∈Ω, also ‖m‖∞=l<∞. We prove the existence of positive solutions under certain conditions.http://www.sciencedirect.com/science/article/pii/S1319516615000067Ecological systemsIndefinite weightGrazing and constant yield harvestingSub–super solution method |
| spellingShingle | Saleh Shakeri Ghasem A. Afrouzi Armin Hadjian On the existence of positive solutions for an ecological model with indefinite weight Arab Journal of Mathematical Sciences Ecological systems Indefinite weight Grazing and constant yield harvesting Sub–super solution method |
| title | On the existence of positive solutions for an ecological model with indefinite weight |
| title_full | On the existence of positive solutions for an ecological model with indefinite weight |
| title_fullStr | On the existence of positive solutions for an ecological model with indefinite weight |
| title_full_unstemmed | On the existence of positive solutions for an ecological model with indefinite weight |
| title_short | On the existence of positive solutions for an ecological model with indefinite weight |
| title_sort | on the existence of positive solutions for an ecological model with indefinite weight |
| topic | Ecological systems Indefinite weight Grazing and constant yield harvesting Sub–super solution method |
| url | http://www.sciencedirect.com/science/article/pii/S1319516615000067 |
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