Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 19, pp. 1-10.
Title: Existence of solutions to nonlocal and singular elliptic
problems via Galerkin method
Authors: Francisco Julio S. A. Correa (Univ. Federal do Para, Brazil)
Silvano D. B. Menezes (Univ. Federal do Para, Brazil)
Abstract:
We study the existence of solutions to the nonlocal elliptic equation
$$
-M(\|u\|^2)\Delta u = f(x,u)
$$
with zero Dirichlet boundary conditions on a bounded and smooth
domain of $\mathbb{R}^n$.
We consider the $M$-linear case with $f\in H^{-1}(\Omega )$,
and the sub-linear case $f(u)=u^{\alpha}$, $0<\alpha <1$.
Our main tool is the Galerkin method for both cases when $M$
continuous and when $M$ is discontinuous.
Submitted December 15, 2003. Published February 11, 2004.
Math Subject Classifications: 35J60, 35J25.
Key Words: Nonlocal elliptic problems; Galerkin Method.