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Liouville theorems for quasilinear differential inequalities involving gradient nonlinearity term on manifolds
孙玉华 副教授(南开大学)
2021年4月30日13:30-14:30  腾讯会议ID:491 801 880

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We investigate the nonexistence and existence of nontrivial positive solutions to

$\Delta_m u+u^p|\nabla u|^q\leq0$ on noncompact geodesically complete Riemannian manifolds, where $m>1$, and $(p,q)\in \mathbb{R}^2$.

According to a complete classification of $(p, q)$, we establish different volume growth conditions to obtain Liouville theorems for the above quasilinear differential inequalities, and we also show these volume growth conditions are sharp in most cases. Moreover, the results are completely new for $(p, q)$ of negative values, even in the Euclidean space.