Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 160, pp. 1-13.
Title: Existence of weak solutions for degenerate semilinear
elliptic equations in unbounded domains
Authors: Venkataramanarao Raghavendra (Institute of Technology, Kanpur, India)
Rasmita Kar (Institute of Technology, Kanpur, India)
Abstract:
In this study, we prove the existence of a weak solution for
the degenerate semilinear elliptic Dirichlet boundary-value problem
$$\displaylines{
Lu-\mu u g_{1} + h(u) g_{2}= f\quad \hbox{in }\Omega,\cr
u = 0\quad \hbox{on }\partial\Omega
}$$
in a suitable weighted Sobolev space.
Here the domain $\Omega\subset\mathbb{R}^{n}$, $n\geq 3$, is
not necessarily bounded, and $h$ is a continuous bounded
nonlinearity. The theory is also extended for $h$ continuous
and unbounded.
Submitted October 25, 2009. Published December 15, 2009.
Math Subject Classifications: 35J70, 35D30.
Key Words: Degenerate equations; weighted Sobolev space; unbounded domain.