Chipot, M; Voirol, F (1995). On a class of nonlinear elliptic problems with Neumann boundary conditions growing like a power. Zeitschrift für Analysis und ihre Anwendungen, 14(4):853-868.
We investigate the issue of existence and the number of solutions for the problem $\Delta u=au^p$ in $\Omega,\ u=0$ on $\Gamma_0,\ \partial u/\partial n=u^q$ on $\Gamma_1$, where $\Gamma_0$ and $\Gamma_1$ are two parts of the boundary of the open set $\Omega$. In dimension one we are able to find all the solutions to the problem. In higher dimensions we give existence and non-existence results for different solutions depending on $p,q$ and $\Omega$.
We investigate the issue of existence and the number of solutions for the problem $\Delta u=au^p$ in $\Omega,\ u=0$ on $\Gamma_0,\ \partial u/\partial n=u^q$ on $\Gamma_1$, where $\Gamma_0$ and $\Gamma_1$ are two parts of the boundary of the open set $\Omega$. In dimension one we are able to find all the solutions to the problem. In higher dimensions we give existence and non-existence results for different solutions depending on $p,q$ and $\Omega$.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Uncontrolled Keywords: | nonlinear Neumann boundary condition, existence, semilinear elliptic equation |
| Language: | English |
| Date: | 1995 |
| Deposited On: | 26 Aug 2010 10:05 |
| Last Modified: | 23 Jan 2022 14:44 |
| Publisher: | European Mathematical Society |
| ISSN: | 0232-2064 |
| OA Status: | Closed |
Chipot, M