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Lotka-Volterra competition models on finite graphs
Yuanyang Hu, Chengxia Lei
In this paper, we study three two competing species Lotka-Volterra competition models on finite connected graphs, with Dirichlet, Neumann or no boundary conditions. We get that whe…
Prey-Predator models on graphs
Yuanyang Hu, Chengxia Lei
In this paper, we study the Lotka-Volterra prey-predator models consisting of two species on finite connected graphs under Neumann condition and the condition that there is no boun…
Monotone methods for semilinear parabolic and elliptic equations on graphs
Yuanyang Hu, Chengxia Lei
This paper is devoted to investigate the extinction and propagation properties of solutions to the graph Laplacian parabolic problems with Kpp type or Allen-Cahn type forcing terms…
Existence of solutions to relativistic non-Abelian Chern-Simons-Higgs vortex equations on graphs
Yuanyang Hu
Let be a connected finite graph. We study the relativistic non-Abelian Chern-Simons-Higgs vortex equations on the graph . We establish an existence result to the relat…
Existence and uniqueness of solutions to non-Abelian multiple vortex equations on graphs
Yuanyang Hu
Let be a connected finite graph. We study a system of non-Abelian multiple vortex equations on . We established a necessary and sufficient condition for the existence…
Existence and uniqueness of solutions to Bogomol'nyi-Prased-Sommerfeld equations on graphs
Yuanyang Hu
Let be a connected finite graph. We investigate two Bogomol'nyi-Prased-Sommerfeld equations on . We establish necessary and sufficient conditions for the existence and…
Existence and uniqueness of solutions to Bogomol'nyi equations on graphs
Yuanyang Hu
Let be a connected finite graph. We study the Bogomol'nyi equation \begin{equation*} Δu= \mathrm{e}^{u}-1 +4 π\sum_{s=1}^{k} n_s δ_{z_{s}} \quad \text { on } \quad G, \en…
Existence of solutions to a generalized self-dual Chern-Simons equation on finite graphs
Yuanyang Hu
Let be a connected finite graph. We study the existence of solutions for the following generalized Chern-Simons equation on \begin{equation*} Δu=λ\mathrm{e}^{u}\left(…