A nonlocal elliptic equation in a bounded domain
Volume 66 / 2004
Banach Center Publications 66 (2004), 127-133
MSC: Primary 35J65.
DOI: 10.4064/bc66-0-8
Abstract
The existence of a positive solution to the Dirichlet boundary value problem for the second order elliptic equation in divergence form $$-\sum_{i,j=1}^{n}D_i(a_{ij}D_ju) =f\bigg(u,\int_{\Omega}g(u^p)\bigg),$$ in a bounded domain $\Omega$ in ${\mathbb R}^n$ with some growth assumptions on the nonlinear terms $f$ and $g$ is proved. The method based on the Krasnosel'ski\uı Fixed Point Theorem enables us to find many solutions as well.
