13 papers
Sharp Born--Infeld Sobolev inequality and extremal functions on the lattice graph
Chao Ji, Kai Sheng
In this paper, we study the sharp Sobolev-type inequality associated with the Born--Infeld energy on the lattice graph \(\mathbb Z^N\), \(N\geq3\): \[ \frac12\sum_{x\in\mathbb Z^N}…
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 (…
A partial answer to Brezis' Open Problem 2.1
Chao Ji, Kai Sheng
In this paper, we give a partial answer to Brezis' Open Problem~2.1, which concerns the uniqueness of solutions to the Ginzburg--Landau equation in the unit disc with the degree-on…
Singular limit of lattice graphs and its application to critical Lane--Emden equations on lattice graphs
Zhentao He, Chao Ji
In this paper, we establish new connections between lattice graphs and metric grids, providing a unified framework for the study of singular limit problems and Gagliardo--Nirenberg…
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 we prove the self-adjointness of its corr…
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…
Existence and multiplicity of normalized solutions for the generalized Kadomtsev-Petviashvili equation in
Claudianor O. Alves, Rui Ding, Chao Ji
In this paper, we study the existence and {multiplicity} of nontrivial solitary waves for the generalized Kadomtsev-Petviashvili equation with prescribed {-norm} \begin{equati…
Existence and multiplicity of normalized solutions for -Laplacian equations with generic double-behaviour nonlinearities
Rui Ding, Chao Ji, Patrizia Pucci
In this paper, we study {existence and multiplicity} of normalized solutions for the following -Laplacian equation \begin{equation*}\label{Eq-Equation1} \left\{\begin{array…
Normalized solutions to a class of -Laplacian equationsin the strongly sublinear regime
Rui Ding, Chao Ji, Patrizia Pucci
In this paper, we consider the existence and multiplicity of normalized solutions for the following -Laplacian equation \begin{equation}\label{Equation1} \left\{\begin{alig…
Nodal solutions for the double phase problems
Chao Ji, Nikolaos S. Papageorgiou
We consider a parametric nonautonomous -equation with unbalanced growth as follows \begin{align*} \left\{ \begin{aligned} &-Δ_p^αu(z)-Δ_q u(z)=λ\vert u(z)\vert^{τ-2}u(z)+f(…