8 citations · 13 across the 13 of their papers we have counts for
15 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…
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…
BGD domains in p.c.f. self-similar sets II: spectral asymptotics for Laplacians
Qingsong Gu, Hua Qiu
Let be a p.c.f. self-similar set equipped with a strongly recurrent Dirichlet form. Under a homogeneity assumption, for an open set whose boundary is…
BGD domains in p.c.f. self-similar sets I: boundary value problems for harmonic functions
Qingsong Gu, Hua Qiu
We study the boundary value problems for harmonic functions on open connected subsets of post-critically finite (p.c.f.) self-similar sets, on which the Laplacian is defined throug…
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…
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…
-energies on p.c.f. self-similar sets
Shiping Cao, Qingsong Gu, Hua Qiu
We study -energies on post critically finite (p.c.f.) self-similar sets for , as limits of discrete -energies on approximation graphs, extending the construction…
On nonexistence and existence of positive global solutions to heat equation with a potential term on Riemannian manifolds
Qingsong Gu, Yuhua Sun, Fanheng Xu
We reinvestigate nonexistence and existence of global positive solutions to heat equation with a potential term on Riemannian manifolds. Especially, we give a very natural sharp co…
Metrics on the Sierpinski carpet by weight functions
Qingsong Gu, Hua Qiu, Huo-Jun Ruan
We construct certain metrics on the Sierpinski carpet via a class of self-similar weight functions. Using these metrics and by applying known results, we obtain the two-sided sub-G…
On a recursive construction of Dirichlet form on the Sierpiński gasket
Qingsong Gu, Ka-Sing Lau, Hua Qiu
Let denote the -th level Sierpiński graph of the Sierpiński gasket . We consider, for any given conductance on , the Dirchlet form …
Dirichlet forms and critical exponents on fractals
Qingsong Gu, Ka-Sing Lau
Let denote the Besov space defined on a compact set which is equipped with an -regular measure . The {\it critical exponent} is…
Lipschitz invariance of walk dimension on connected self-similar sets
Hui Rao, Qingsong Gu
Walk dimension is an important conception in analysis of fractals. In this paper we prove that the walk dimension of a connected compact set possessing an Alfors regular measure is…