Electron. J. Diff. Eqns., Vol. 1998(1998), No. 01, pp. 1-27.

Existence of continuous and singular ground states for semilinear elliptic systems

Cecilia S. Yarur

We study existence results of a curve of continuous and singular ground states for the system
$$ \eqalign{
  -\Delta{u}  &=  {\alpha(|x|)}f(v) \cr
  -\Delta{v}  &=  \beta(|x|) g(u)\,. \cr }$$
where $x \in {\Bbb R}^N \setminus \{0\}$, the functions f and g are increasing Lipschitz continuous functions in $\Bbb R$, and $\alpha$ and $\beta$ are nonnegative continuous functions in ${\Bbb R}^+$. We also study general systems of the form
$$ \eqalign{
  \Delta u(x)+V(|x|)u+a(|x|)v^p &= 0 \cr
  \Delta v(x)+V(|x|)v+b(|x|)u^q &= 0\,.\cr} $$

Submitted September 3, 1997. Published January 16, 1998.
Math Subject Classification: 35J60, 31A35.
Key Words: Semilinear elliptic systems, ground states.

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Cecilia S. Yarur
Departamento de Matematica y C. C., Universidad de Santiago de Chile
Casilla 307, Correo 2, Santiago, Chile
e-mail: cyarur@fermat.usach.cl
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