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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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 |
| Summary: | 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.
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| ISSN: | 1120-7183 2532-3350 |