Q-curvature flow with indefinite nonlinearity

Abstract

In this Note, we study Q-curvature flow on S 4 with indefinite nonlinearity. Our result is that the prescribed Q-curvature problem on S 4 has a solution provided the prescribed non-negative Q-curvature f has its positive part, which possesses non-degenerate critical points such that Δ S 4 f ≠ 0 at the saddle points and an extra condition such as a nontrivial degree counting condition.