Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 01, pp. 1-27.
Title: Existence of continuous and singular ground states
for semilinear elliptic systems
Author: Cecilia S. Yarur (Univ. de Santiago de Chile, Chile)
Abstract:
We study existence results of a curve of continuous and singular
ground states for the system
$$ \eqaling{
-\Delta{u} &= {\alpha(|x|)}f(v) \cr
-\Delta{v} &= \beta(|x|) g(u)\,. \cr }$$
where $x \in R^N \setminus \{0\}$, the functions $f$ and $g$ are
increasing Lipschitz continuous functions in $R$,
and $\alpha$ and $\beta$ are nonnegative continuous functions in
$R^+$. We also study general systems of the form
$$ \eqaling{
\Delta u(x)+V(|x|)u+a(|x|)v^p &= 0 \cr
\Delta v(x)+V(|x|)v+b(|x|)u^q &= 0\,.\cr} $$
Submitted September 3, 1997. Published January 16, 1998.
Math Subject Classification: 35J60, 31A35.
Key Words: Semilinear elliptic systems; ground states.