8 papers
Normalized solutions of -supercritical NLS equations with periodic potentials
Zhentao He, Norihisa Ikoma, Chao Ji
In this paper, we study normalized solutions to the following -supercritical nonlinear Schrödinger equation with a periodic potential \begin{equation*} \begin{dcases} -Δu +V (…
Normalized solutions of nonlinear magnetic Schrödinger equations on metric graphs
Pietro d'Avenia, Zhentao He, Chao Ji
In this paper we first establish the theory of a magnetic Sobolev space on metric graphs and prove the self-adjointness of the associa…
Normalized solutions for -supercritical Schrödinger equations with nonlinear point defects on noncompact metric graphs
Zhentao He, Chao Ji, Yifan Tao
In this paper, we study the existence and multiplicity of normalized solutions for the following -supercritical Schrödinger equation with nonlinear point defects on a noncompa…
Nonrelativistic limit of normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities
Zhentao He, Chao Ji
In this paper, we study the nonrelativistic limit of normalized solutions for the following nonlinear Dirac equation (NLDE) on noncompact metric graph $\G$ with finitely many edges…
Existence and multiplicity of normalized solutions to a large class of elliptic equations on bounded domains with general boundary conditions
Claudianor O. Alves, Zhentao He, Chao Ji
In this paper, by adapting the perturbation method, we study the existence and multiplicity of normalized solutions for the following nonlinear Schrödinger equation $$ \left\{ \beg…
Existence of normalized solutions to nonlinear Schrödinger equations on lattice graphs
Zhentao He, Chao Ji, Yifan Tao
In this paper, using a discrete Schwarz rearrangement on lattice graphs developed in \cite{DSR}, we study the existence of global minimizers for the following functional $I:H^1\lef…
Normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities
Zhentao He, Chao Ji
In this paper, we study the following nonlinear Dirac equations (NLDE) on noncompact metric graph with localized nonlinearities \begin{equation} \mathcal{D} u - ωu= a…
The double phase problems on lattice graphs
Zhentao He, Chao Ji
In this paper, we first develop the theory of Musielak-Orlicz spaces on locally finite graphs, including completeness, reflexivity, separability, and so on. Then, we give some elem…