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arXiv · 2205.06047

Sharp Liouville type results for semilinear elliptic inequalities involving gradient terms on weighted graphs

Lu Hao·Yuhua Sun
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Abstract

We study nonexistence and existence of nontrivial positive solutions to the following semilinear elliptic inequality involving gradient terms \[ \Delta u+u^p\left|\nabla u\right|^q\leq0, \] on weighted graphs, where $(p,q)\in\mathbb{R}^2$. We give a complete classification of $(p,q)$ under which sharp volume growth assumptions are established.

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Lu Hao, Yuhua Sun. 2022-05-12. Sharp Liouville type results for semilinear elliptic inequalities involving gradient terms on weighted graphs. https://arxiv.org/abs/2205.06047

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