247 citations · 892 across the 38 of their papers we have counts for
9 papers · 1 filter
Sobolev spaces on locally finite graphs
Mengqiu Shao, Yunyan Yang, Liang Zhao
In this paper, we develop the theory of Sobolev spaces on locally finite graphs, including completeness, reflexivity, separability, and Sobolev inequalities. Since there is no exac…
Existence and convergence of solutions to -Laplace equations on locally finite graphs
Mengqiu Shao, Yunyan Yang, Liang Zhao
We are mainly concerned with the nonlinear -Laplace equation \begin{equation*} -Δ_pu+ρ|u|^{p-2}u=ψ(x,u) \end{equation*} on a locally finite graph , where belongs to…
Normalized solutions for nonlinear Schrödinger equations on graphs
Yunyan Yang, Liang Zhao
We are concerned with the nonlinear Schrödinger equation with an mass constraint on both finite and locally finite graphs and prove that the equation has a normalized solutio…
Global Convergence and Error Estimates in Infinity-ion-mass Limits for Bipolar Euler-Poisson System
Yachun Li, Shihao Wang, Liang Zhao
This paper is concerned with the global-in-time convergence from bipolar Euler-Poisson system (BEP) to unipolar one (UEP) through the infinity-ion-mass limit by letting the ratio o…
Normalized solution to the nonlinear p-Laplacian equation with an L^2 constrain: mass supercritical case
Yulu Tian, Deng-Shan Wang, Liang Zhao
In this paper, we study the existence of ground state solutions to the following p-Laplacian equation in some dimension with an constraint: \begin{equation*} \begin{…
Existence and convergence of solutions for nonlinear elliptic systems on graphs
Jinyan Xu, Liang Zhao
We consider a kind of nonlinear systems on a locally finite graphs . We prove via the mountain pass theorem that this kind of systems has a nontrivial ground state solutio…