Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulus
We study the boundary value problem −∆u(x) = λf(u(x)), R< |x| < Rˆ u(x)=0, |x| ∈ {R, Rˆ} where λ > 0, f(0) < 0 and f is superlinear. We prove existence of a radially symmetric non-negative solution for λ > 0 sufficiently small and nonexistence of such a solution for λ > 0 larg...
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| Format: | Article |
| Language: | English |
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Sapienza Università Editrice
1994-03-01
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| Series: | Rendiconti di Matematica e delle Sue Applicazioni |
| Subjects: | |
| Online Access: | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1994(4)/625-646.pdf |
| _version_ | 1797810821288427520 |
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| author | D. ARCOYA A. ZERTITI |
| author_facet | D. ARCOYA A. ZERTITI |
| author_sort | D. ARCOYA |
| collection | DOAJ |
| description | We study the boundary value problem
−∆u(x) = λf(u(x)), R< |x| < Rˆ
u(x)=0, |x| ∈ {R, Rˆ}
where λ > 0, f(0) < 0 and f is superlinear. We prove existence of a radially symmetric
non-negative solution for λ > 0 sufficiently small and nonexistence of such a solution
for λ > 0 large.
|
| first_indexed | 2024-03-13T07:14:34Z |
| format | Article |
| id | doaj.art-fd84a6f7adaf4de38e077b8060ba3303 |
| institution | Directory Open Access Journal |
| issn | 1120-7183 2532-3350 |
| language | English |
| last_indexed | 2024-03-13T07:14:34Z |
| publishDate | 1994-03-01 |
| publisher | Sapienza Università Editrice |
| record_format | Article |
| series | Rendiconti di Matematica e delle Sue Applicazioni |
| spelling | doaj.art-fd84a6f7adaf4de38e077b8060ba33032023-06-05T14:38:47ZengSapienza Università EditriceRendiconti di Matematica e delle Sue Applicazioni1120-71832532-33501994-03-01144625646Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulusD. ARCOYA 0A. ZERTITI1Departamento de Analisis Matematico – Universidad de Granada – 18071 Granada, SpainUniversité Abdelmalek Essaadi – Faculté des Sciences – Departement de Mathematiques – BP2121 Tetouan, MarocWe study the boundary value problem −∆u(x) = λf(u(x)), R< |x| < Rˆ u(x)=0, |x| ∈ {R, Rˆ} where λ > 0, f(0) < 0 and f is superlinear. We prove existence of a radially symmetric non-negative solution for λ > 0 sufficiently small and nonexistence of such a solution for λ > 0 large. https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1994(4)/625-646.pdfsuperlinear semi-positone problemsradial positive solution |
| spellingShingle | D. ARCOYA A. ZERTITI Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulus Rendiconti di Matematica e delle Sue Applicazioni superlinear semi-positone problems radial positive solution |
| title | Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulus |
| title_full | Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulus |
| title_fullStr | Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulus |
| title_full_unstemmed | Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulus |
| title_short | Existence and non-existence of radially symmetric non-negative solutions for a class of semi-positone problems in an annulus |
| title_sort | existence and non existence of radially symmetric non negative solutions for a class of semi positone problems in an annulus |
| topic | superlinear semi-positone problems radial positive solution |
| url | https://www1.mat.uniroma1.it/ricerca/rendiconti/ARCHIVIO/1994(4)/625-646.pdf |
| work_keys_str_mv | AT darcoya existenceandnonexistenceofradiallysymmetricnonnegativesolutionsforaclassofsemipositoneproblemsinanannulus AT azertiti existenceandnonexistenceofradiallysymmetricnonnegativesolutionsforaclassofsemipositoneproblemsinanannulus |