6 papers · 1 filter
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 \[ -Îu\ge v^p,\qquad -Îv\ge u^q, \qquad p,q>0,\quad pq>1, \] 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 \[ -Î_p u\ge Ï(x)u^q \] on infinite locally finite connected weighted graphs, whe…
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 \[ -Îu\ge Ïu^q,\qquad q>1, \] on infinite locally finite weighted graphs and connected domains. When the Dir…
On Brezis Open Problem 3.1
Qi Guo, Xueping Huang, Yi C. Huang +2
Let be the unit disk in . We consider the harmonic map equation subject to the Dirichlet boundary condition $ u(e^{iθ})=(R\cosθ,R\si…
The Ekeland--Nirenberg Variational Problem:A Sharp Positivity Threshold and Extensions
Qi Guo, Xueping Huang, Yi Huang
We study the Ekeland--Nirenberg variational problem in the two-dimensional diagonal family \[ J_{a,c,d}(u)=\int_{\Rp^2}\bigl(u_{xy}^2+a u_x^2+c u_y^2+d u^2\bigr)\dd x\dd y, \qquad…