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On partially free boundary solutions for elliptic problems with non-Lipschitz nonlinearities
Applied Mathematics Letters, 95, (2019) 23-28 We show that the elliptic equation with a non-Lipschitz right-hand side, $-\Delta u = \lambda |u|^{\beta-1}u - |u|^{\alpha-1}u$ with $\lambda>0$ and $0<\alpha<\beta<1$, considered on a smooth star-shaped domain $\Omega$ subject to zero Dirich...
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| Main Authors | , , |
|---|---|
| Format | Journal Article |
| Language | English |
| Published |
19.12.2018
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.1812.08018 |
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| Summary: | Applied Mathematics Letters, 95, (2019) 23-28 We show that the elliptic equation with a non-Lipschitz right-hand side,
$-\Delta u = \lambda |u|^{\beta-1}u - |u|^{\alpha-1}u$ with $\lambda>0$ and
$0<\alpha<\beta<1$, considered on a smooth star-shaped domain $\Omega$ subject
to zero Dirichlet boundary conditions, might possess a nonnegative ground state
solution which violates Hopf's maximum principle only on a nonempty subset
$\Gamma$ of the boundary $\partial\Omega$ such that $\Gamma \neq
\partial\Omega$. |
|---|---|
| DOI: | 10.48550/arxiv.1812.08018 |