  In this paper, we consider the indefinite scalar curvature problem on $R^n$.
We propose new conditions on the prescribing scalar curvature function such
that the scalar curvature problem on $R^n$ (similarly, on $S^n$) has at least
one solution. The key observation in our proof is that we use the bifurcation
method to get a large solution and then after establishing the Harnack
inequality for solutions near the critical points of the prescribed scalar
curvature and taking limit, we find the nontrivial positive solution to the
indefinite scalar curvature problem.
