6 papers
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}^…
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…