11 papers
Flow decomposition and stochastic completeness of weighted graphs
Qingsong Gu, Lu Hao, Xueping Huang +1
We give a new proof by flow decomposition of the known Grigor'yan type integral criterion for stochastic completeness of weighted graphs. The main ingredient is a finite-domain est…
Flow Decomposition and Sharp Integral Fujita Criteria on Weighted Graphs
Qingsong Gu, Lu Hao, Xueping Huang +1
We study the Fujita phenomenon for semilinear heat inequalities generated by variable-speed Laplacians on infinite weighted graphs. Assuming that the graph carries a proper adapted…
A sharp integral criterion for the Lane--Emden system of inequalities on weighted graphs
Qingsong Gu, Lu Hao, Xueping Huang +1
We establish a sharp integral nonexistence criterion for the Lane--Emden system of inequalities \[ -Δu\ge v^p,\qquad -Δv\ge u^q, \qquad p,q>0,\quad pq>1, \] on arbitrary infinite,…
A Volume-Growth Criterion for the p-Laplace Inequality on Weighted Graphs
Qingsong Gu, Lu Hao, Xueping Huang +1
We prove a nonexistence result for nonnegative solutions of the quasi-linear elliptic inequality \[ -Δ_p u\ge σ(x)u^q \] on infinite locally finite connected weighted graphs, where…
Mixed-Parabolicity and Mixed-Liouville Property for Products of Riemannian Manifolds
Liguang Liu, Yuhua Sun, Suqing Wu
Let and be the product of two geodesically complete Riemannian manifolds. In this paper, the authors first develop an anisotropic potential…
Liouville Type Results for Quasilinear Elliptic Inequalities Involving Gradient Terms on Weighted Graphs
Anh Tuan Duong, Yao Liu, Nguyên Công Minh +2
In this paper, we study the following quasi-linear elliptic inequality on weighted graphs, where $(m,p,q)\in (1,\infty)\times\mathbb{R}\times\…
Flow Decomposition, Green Testing, and Lane--Emden Inequalities on Weighted Graphs
Qingsong Gu, Lu Hao, Xueping Huang +1
We study positive solutions of the superlinear Lane--Emden inequality \[ -Δu\ge σu^q,\qquad q>1, \] on infinite locally finite weighted graphs and connected domains. When the Diric…
Sharp criteria for nonlocal elliptic inequalities on manifolds
Qingsong Gu, Xueping Huang, Yuhua Sun
Let be a complete non-compact Riemannian manifold and be a Radon measure on , we study the existence and non-existence of positive solutions to a nonlocal elliptic inequ…
A priori estimates and Liouville type results for quasilinear elliptic equations involving gradient terms
Roberta Filippucci, Yuhua Sun, Yadong Zheng
In this article we study local and global properties of positive solutions of in a domain of , with , and $M\in\mathb…
On positive solutions of biharmonic elliptic inequalities on Riemannian manifolds
Yuhua Sun, Yadong Zheng
We investigate the non-existence and existence of positive solutions to biharmonic elliptic inequalities on manifolds. Using Green function and volume growth conditions, we establi…
Superlinear elliptic inequalities on weighted graphs
Qingsong Gu, Xueping Huang, Yuhua Sun
Let be an infinite, connected, locally finite weighted graph. We study the problem of existence or non-existence of positive solutions to a semi-linear elliptic inequality…