Non-local Gel'fand problem in higher dimensions
Volume 66 / 2004
Banach Center Publications 66 (2004), 221-235
MSC: 35J60, 35P30, 35J20.
DOI: 10.4064/bc66-0-15
Abstract
The non-local Gel'fand problem, $\Delta v + \lambda e^v/\! \int_{\Omega}e^vdx= 0$ with Dirichlet boundary condition, is studied on an $n$-dimensional bounded domain $\Omega$. If it is star-shaped, then we have an upper bound of $\lambda$ for the existence of the solution. We also have infinitely many bendings in $\lambda$ of the connected component of the solution set in $\lambda, v$ if $\Omega$ is a ball and $3\leq n\leq 9$.
