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math.AP2024
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: $$ Δu = λe^u (e^u - 1)^{2p+1} +…
math.AP2022
Multiple solutions of a nonlinear biharmonic equation on graphs
Songbo Hou
In this paper, we consider a biharmonic equation with respect to the Dirichlet problem on a domain of a locally finite graph. Using the variation method, we prove that the equation…
math.AP2022
Existence of solutions to Chern-Simons-Higgs equations on graphs
Songbo Hou, Jiamin Sun
Let be a finite graph. We consider the existence of solutions to a generalized Chern-Simons-Higgs equation $$ Δu=-λe^{g(u)}\left( e^{g(u)}-1\right)^2+4π\sum\limits_{j=1}^…