Non-local Gel'fand problem in higher dimensions
Tosiya Miyasita, Takashi Suzuki · Banach Center Publications · 2004
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 existenc