Electron. J. Diff. Eqns., Vol. 1996(1996), No. 08, pp. 1-22.

Nonexistence of Positive Singular Solutions for a Class of Semilinear Elliptic Systems

Cecilia S. Yarur

Abstract:
We study nonexistence and removability results for nonnegative sub-solutions to
$$\left. \eqalign{ \Delta u =& a(x) v^p \cr \Delta v =& b(x) u^q \cr} \right\} {\rm in } \Omega \subset R^N,\quad N\ge 3\,, $$
where $p\geq 1$, $q\geq 1$, $pq$ greater than 1, and a and b are nonnegative functions. As a consequence of this work, we obtain new results for biharmonic equations.

Submitted June 6, 1996. Published September 6, 1996.
Math Subject Class.: 35J20, 31A35.
Key Words: Elliptic systems, Removable singularity, Biharmonic equation.

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Ceclia S. Yarur
Departamento de Matematicas, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile.
E-mail: cyarur@usach.cl
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