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arXiv · 2604.21145

Liouville Type Results for Quasilinear Elliptic Inequalities Involving Gradient Terms on Weighted Graphs

Anh Tuan Duong·Yao Liu·Nguyên Công Minh·Dao Trong Quyet·Yuhua Sun
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Abstract

In this paper, we study the following quasi-linear elliptic inequality $\Delta_m u +u^p |\nabla u|^q \leqslant 0$ on weighted graphs, where $(m,p,q)\in (1,\infty)\times\mathbb{R}\times\mathbb{R}$. According to the ranges of parameters $(m, p, q)$, we establish the non-existence of nontrivial positive solutions under the corresponding sharp volume growth conditions. Our results can be viewed as a discrete generalization of their counterparts on Riemannian manifolds established by [Sun, Yuhua; Xiao, Jie; Xu, Fanheng, Math. Ann. 384 (2022), no. 3-4, 1309--1341.]. However, this generalization is far from trivial, many results exhibit significant differences from the manifold setting, highlighting the distinct behaviors and challenges that arise in the discrete weighted graph framework.

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Anh Tuan Duong, Yao Liu, Nguyên Công Minh, Dao Trong Quyet, Yuhua Sun. 2026-04-22. Liouville Type Results for Quasilinear Elliptic Inequalities Involving Gradient Terms on Weighted Graphs. https://arxiv.org/abs/2604.21145

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