6 papers · 1 filter
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…