Solutions of second order elliptic equations (Q1179329)

Consider the equations \(\Delta u=K(x)u^ \tau\), \(\tau>1\), respectively \(\Delta u=K(x)e^{2u}\), both on \(\mathbb{R}^ n\). Recall that similar equations appear when one wants to construct on a Riemannian manifold with a metric \(g\) a metric conformally equivalent to \(g\) for which the scalar curvature is a previously given function. A number of results are stated to the effect that under certain assumptions on \(K\) the equations under consideration have no nonnegative or locally bounded solutions.