On the nonexistence of positive solution to Δu + aup+1 = 0 on Riemannian manifolds

Abstract

Inspired by the work of Wang and Zhang [21], we use the Moser iteration to study the nonexistence of positive solution to the semilinear elliptic equationΔu+aup+1=0, defined on complete Riemannian manifold. It is shown in this paper that when the Ricci curvature of manifold is nonnegative and p∈(−∞,2n−1+2n(n−1)), the above equation does not admit positive solution.