Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

Abstract

In this paper, let (Mn,g,dμ) be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation△p,fv+cvσ=0, where c≤0,m>n≥1,1<p<m−1+(m−1)(m+3)2,σ≤p−1 are real constants.