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.