Nonexistence of positive singular solutions for a class of semilinear elliptic systems

sub-solutions to $$left. eqalign{ Delta u =& a(x) v^p cr Delta v =& b(x) u^q cr} ight} { m in } Omega subset Bbb R^N,quad Nge 3,, $$ where $pgeq 1$, $qgeq 1$, $pq>1$, and $a$ and $b$ are nonnegative functions. As a consequence of this work, we obtain new results for biharmonic equations