On the elliptic equation \(\Delta u+Ku^{(n+2)/(n-2)}=0\) and related topics (Q1075505)

The authors consider the equation \[ (1)\quad \Delta u+Ku^{(n+2)/(n- 2)}=0,\quad u>0,\quad n\geq 3 \] in \(R^ n\). When \(K\geq 0\) the situation is more complicated. This paper is to study equation (1) in the case where K is bounded, nonnegative but not necessarily decaying at \(\infty\). For the radial case, they obtain existence and nonexistence results.