5 citations · 9 across the 13 of their papers we have counts for
13 papers
Solutions to a generalized Chern-Simons Higgs model on finite graphs by topological degree
Songbo Hou, Wenjie Qiao
Consider a finite connected graph denoted as . This study explores a generalized Chern-Simons Higgs model, characterized by the equation: $$ Δu = λe^u (e^u - 1)^{2p+1} +…
Existence and asymptotic behaviors of solutions to Chern-Simons systems and equations on finite graphs
Songbo Hou, Xiaoqing Kong
In this paper, we consider a system of equations arising from the Abelian Chern-Simons model \begin{eqnarray*}\left\{\begin{aligned} Δu &=λ\left(a(b…
Existence of solutions to a generalized self-dual Chern-Simons system on finite graphs
Ruixue Chao, Songbo Hou, Jiamin Sun
We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solution…
Multiple solutions of a nonlinear biharmonic equation on graphs
Songbo Hou
In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph. Using the variation method, we prove that the equation…
Existence of solutions to Chern-Simons-Higgs equations on graphs
Songbo Hou, Jiamin Sun
Let be a finite graph. We consider the existence of solutions to a generalized Chern-Simons-Higgs equation $$ Δu=-λe^{g(u)}\left( e^{g(u)}-1\right)^2+4π\sum\limits_{j=1}^…
Existence theorems for a generalized Chern-Simons equation on finite graphs
Jia Gao, Songbo Hou
Denote by a finite graph. We study a generalized Chern-Simons equation on , where and …
Eigenvalues of the Laplace operator with potential under the backward Ricci flow on locally homogeneous 3-manifolds
Songbo Hou, Shusen Yang
Let be the first eigenvalue of under the backward Ricci flow on locally homogeneous 3-manifolds, where is the scalar curvature. In the Bianchi case, we g…
Gradient estimates for the nonlinear parabolic equation with two exponents on Riemannian manifolds
Songbo Hou
In this paper, we study the nonlinear parabolic equation with two exponents on complete noncompact Riemannian maniflods. The special types of such equation include the Fisher-KPP e…
Extremal functions for a singular Hardy-Moser-Trudinger inequality
Songbo Hou
In this paper, using blow-up analysis, we prove a singular Hardy-Morser-Trudinger inequality, and find its extremal functions. Our results extend those of Wang-Ye (Adv. Math. 2012)…
Gradient estimates for the Allen-Cahn equation on Riemannian manifolds
Songbo Hou
In this paper, we consider bounded positive solutions to the Allen-Cahn equation on complete noncompact Riemannian manifolds without boundary. We derive gradient estimates for thos…
Eigenvalues under the backward Ricci flow on locally homogeneous closed 3-manifolds
Songbo Hou
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized backward Ricci flow, construct various quantities which are…
Eigenvalues under the Ricci flow of model geometries
Songbo Hou
In this paper, we study the evolving behaviors of the first eigenvalue of Laplace-Beltrami operator under the normalized Ricci flow of model geometries. In every Bianchi class, we…
Quasi-convergence of the Ricci flow on locally homogeneous closed 4-manifolds
Songbo Hou
We study the quasi-convergence equivalence of some families of metrics on locally homogeneous closed 4-manifolds with trivial isotropy group, and identify the dimension of each equ…