Liouville's theorems to quasilinear differential inequalities involving gradient nonlinearity term on manifolds

Yuhua Sun, Fanheng Xu

We investigate the nonexistence and existence of nontrivial positive solutions to ${\Delta }_{m}u+u^p|\nabla u{|}^q\le 0$ on noncompact geodesically complete Riemannian manifolds, where $m>1$…