Electron. J. Diff. Equ., Vol. 2012 (2012), No. 43, pp. 1-11.

Weak solutions for degenerate semilinear elliptic BVPs in unbounded domains

Rasmita Kar

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.

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Rasmita Kar
Department of Mathematics and Statistics
Indian Institute of Technology
Kanpur, 208016 India
email: rasmi07@gmail.com

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