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

Abstract:
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.

Show me the PDF file (232 KB), TEX file, and other files for this article.

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
Return to the EJDE home page