8 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…
A Wiener criterion at infinity for -massiveness on weighted graphs
Lu Hao
We study boundary value problems at infinity for the graph -Laplacian on infinite, connected, locally finite weighted graphs. Our main result is a Wiener criterion for -massi…
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…
L^p-Parabolicity, the L^q-Liouville Property, and Nonlinear Elliptic Systems on Weighted Graphs
Lu Hao, Yuhua Sun
We establish an equivalence between -parabolicity, the -Liouville property for nonnegative superharmonic functions, and the rigidity of nonnegative solutions to the ellip…
Sharp Liouville type results for semilinear elliptic inequalities involving gradient terms on weighted graphs
Lu Hao, Yuhua Sun
We study nonexistence and existence of nontrivial positive solutions to the following semilinear elliptic inequality involving gradient terms \[ Δu+u^p\left|\nabla u\right|^q\leq0,…