Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 43, pp. 1-11.

Title: Weak solutions for degenerate semilinear elliptic BVPs in
       unbounded domains

Author: Rasmita Kar (Indian Inst. of Technology, Kanpur, India)

Abstract:
 In this article, we prove the existence of a weak solution for the
 degenerate semilinear elliptic Dirichlet boundary-value problem
 $$\displaylines{
  Lu(x)+\sum_{i=1}^n g(x)h(u(x))D_iu(x)=f(x)\quad \hbox{in }\Omega,\cr
  u=0\quad \hbox{on }\partial\Omega,
 }$$
 in a suitable weighted Sobolev space. Here
 $\Omega\subset\mathbb{R}^n$, $1\leq n\leq3,$ is not necessarily bounded.
 
Submitted September 17, 2011. Published March 20, 2012.
Math Subject Classifications: 46E35, 35J61.
Key Words: Semilinear elliptic boundary value problem; unbounded domain;
           pseudomonotone operator.