陈志杰｜清华大学｜学者主页

百晓学者学者目录

精选作品

期刊论文

2026

Green functions, Hitchin's formula, and curvature equations on tori II: Rectangular torus

Zhijie Chen, Erjuan Fu, Chang‐Shou Lin

Proceedings of the London Mathematical Society

DOI

2026

Proof of a conjecture of Dahmen and Beukers on counting integral Lamé equations with finite monodromy

Zhijie Chen, Ting-Jung Kuo, Chang‐Shou Lin

Advances in Mathematics

DOI

2025

Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents

Zhijie Chen, Junzhao Yu

Calculus of Variations and Partial Differential Equations

DOI

2025

Asymptotic behaviors of least energy solutions for weakly coupled nonlinear Schrödinger systems

Zhijie Chen, Ze-Tao Cheng

Advanced Nonlinear Studies

DOI

2025

Existence of solutions to a strongly coupled system for the curl-curl operator with critical exponent

Zhijie Chen, Zhen Song, Zhaoji Zhang

Discrete and Continuous Dynamical Systems

DOI

2025

Concentration phenomena of positive solutions to weakly coupled Schrödinger systems with large exponents in dimension two

Zhijie Chen, Hanqing Zhao

Journal of Differential Equations

DOI

2025

Monodromy of a generalized Lamé equation of third order

Zhijie Chen, Chang‐Shou Lin

Mathematische Annalen

DOI

2024

Existence of solutions to Hamilton systems for the curl–curl operator with subcritical nonlinearities

Zhijie Chen, Zhen Song, Zhaoji Zhang

Annali di Matematica Pura ed Applicata

DOI

2024

Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two

Zhijie Chen, Zetao Cheng, Hanqing Zhao

Calculus of Variations and Partial Differential Equations

DOI

2024

On the closure of the Airault–Mckean–Moser locus for elliptic KdV potentials via Darboux transformations

Zhijie Chen, Ting-Jung Kuo, Chang‐Shou Lin

Journal of Spectral Theory

DOI

2024

Energy quantization of the two dimensional Lane-Emden equation with vanishing potentials

Zhijie Chen, Houwang Li

Journal of Functional Analysis

DOI

2024

Critical points of the Eisenstein series $E_{4}$ and application to the spectrum of the Lamé operator

Zhijie Chen, Chang‐Shou Lin

Journal of Spectral Theory

DOI

2024

Co-Axial Metrics on the Sphere and Algebraic Numbers

Zhijie Chen, Chang‐Shou Lin, Yifan Yang

Symmetry Integrability and Geometry Methods and Applications

DOI

2024

Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, II

Zhijie Chen, Chang‐Shou Lin

Journal of Differential Geometry

DOI

2023

Asymptotic behavior of least energy nodal solutions for biharmonic Lane–Emden problems in dimension four

Zhijie Chen, Zetao Cheng, Hanqing Zhao

Calculus of Variations and Partial Differential Equations

DOI

2023

On number and evenness of solutions of the $SU(3)$ Toda system on flat tori with non-critical parameters

Zhijie Chen, Chang‐Shou Lin

Journal of Differential Geometry

DOI

2022

Sharp upper bound of the number of solutions for the SU(N + 1) Toda system on torus with non-critical parameters

Zhijie Chen, Jia-Wei Guo, Chang‐Shou Lin

Journal of Functional Analysis

DOI

2021

Spectrum of the Lamé operator and application, I: Deformation along Re τ = 1 2

Zhijie Chen, Erjuan Fu, Chang‐Shou Lin

Advances in Mathematics

DOI

2021

The geometry of generalized Lamé equation, III: One-to-one of the Riemann–Hilbert correspondence

Zhijie Chen, Ting-Jung Kuo, Chang‐Shou Lin

Pure and Applied Mathematics Quarterly

DOI

2020

Spectrum of the Lamé Operator and Application, II: When an Endpoint is a Cusp

Zhijie Chen, Chang‐Shou Lin

Communications in Mathematical Physics

DOI

2019

On Algebro-Geometric Simply-Periodic Solutions of the KdV Hierarchy

Zhijie Chen, Chang‐Shou Lin

Communications in Mathematical Physics

DOI

2019

The geometry of generalized Lamé equation, II: Existence of pre-modular forms and application

Zhijie Chen, Ting-Jung Kuo, Chang‐Shou Lin

Journal de Mathématiques Pures et Appliquées

DOI

2019

Simple zero property of some holomorphic functions on the moduli space of tori

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin

Science China Mathematics

2018

The geometry of generalized Lamé equation, I

Zhijie Chen, Ting-Jung Kuo, Chang‐Shou Lin

Journal de Mathématiques Pures et Appliquées

DOI

2017

Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I

Zhijie Chen, Ting-Jung Kuo, Chang‐Shou Lin

Journal of Geometry and Physics

DOI

2013

Standing waves for coupled nonlinear Schrödinger equations with decaying potentials

Zhijie Chen, Wenming Zou

Journal of Mathematical Physics

DOI

2013

Standing waves for a coupled system of nonlinear Schrödinger equations

Zhijie Chen, Wenming Zou

Annali di Matematica Pura ed Applicata (1923 -)

DOI

预印本

2026

Sharp weighted Carleman and Huber isoperimetric inequalities on the unit ball in higher dimensions

Zhijie Chen, Changfeng Gui, Shihong Zhang

arXiv preprint

2026

Qualitative analysis of positive singular solutions for a critical elliptic system in a punctured ball

Zhijie Chen, Hui Yang, Junzhao Yu

arXiv preprint

2026

Liouville theorems and symmetry of positive solutions for partially confined nonlinear Schrödinger equations

Zhijie Chen, Youjun Wang, Jianjun Zhang, Xuexiu Zhong

arXiv preprint

2026

Sharp criteria for the existence of solutions to curvature equations with two singular sources on rectangular torus

Zhijie Chen, Zhen Song

arXiv (Cornell University)

DOI

2026

Exact counting of spherical metrics with one conical singularity on rectangular tori

Zhijie Chen, Shihong Zhang

arXiv preprint

2026

Geometric analysis on rhombus torus: Green function with two singularities

Zhijie Chen, Erjuan Fu, Chang-Shou Lin, Zhen Song

arXiv preprint

2026

Uniqueness and nonuniqueness for mean field equations with multiple singularities on flat tori

Zhijie Chen, Shihong Zhang

arXiv preprint

2026

Structure of critical points of multiple Green functions on flat torus and applications

Zhijie Chen, Chang-Shou Lin

arXiv preprint

2026

On the Classification of blow-up solutions of a singular Liouville equation on the disk

Zhijie Chen, Houwang Li, Tuoxin Li, Juncheng Wei

arXiv preprint

2025

Critical points of the Moser-Trudinger functional on conical singular surfaces, I: compactness

Zhijie Chen, Houwang Li

arXiv (Cornell University)

DOI

2025

Sharp stability on the second Robin eigenvalue with negative boundary parameters

Zhijie Chen, Zhen Song, Wenming Zou

arXiv (Cornell University)

DOI

2025

Sovability of curvature equations with multiple singular sources on torus via Painleve VI equations

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin

arXiv preprint

2025

Generic non-degeneracy of critical points of multiple Green functions on torus and applications to curvature equations

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

arXiv preprint

2025

On the distribution of critical points of the Eisenstein series $E_6$ and monodromy interpretation

Zhijie Chen

arXiv preprint

2024

Monodromy of generalized Lame equations with Darboux-Treibich-Verdier potentials: A universal law

Zhijie Chen, Chang-Shou Lin

arXiv preprint

2022

Sharp estimates, uniqueness and nondegeneracy of positive solutions of the Lane-Emden system in planar domains

Zhijie Chen, Houwang Li, Wenming Zou

arXiv preprint

2022

Asymptotic behavior of positive solutions to the Lane-Emden system in dimension two

Chen Zhijie, Li Houwang, Zou Wenming

arXiv preprint

2021

Modular Ordinary Differential Equations on ${\rm SL}(2,\mathbb{Z})$ of Third Order and Applications

Zhijie Chen, Chang-Shou Lin, Yifan Yang

arXiv preprint

DOI

2020

A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $\mathbb{R}$

Zhijie Chen, Erjuan Fu, Chang-Shou Lin

arXiv preprint

2017

Sharp nonexistence results for curvature equations with four singular sources on rectangular tori

Zhijie Chen, Chang-Shou Lin

arXiv preprint

2017

Critical points of the classical Eisenstein series of weight two

Zhijie Chen, Chang-Shou Lin

arXiv preprint

2016

On reducible monodromy representations of some generalized Lamé equation

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin, Kouichi Takemura

arXiv preprint

DOI

2016

Non-existence of solutions for a mean field equation on flat tori at critical parameter $16π$

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin

arXiv preprint

2016

Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin, Kouichi Takemura

arXiv preprint

DOI

2015

Hamiltonian system for the elliptic form of Painlevé VI equation

Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin

arXiv preprint

2014

Removable singularity of positive solutions for a critical elliptic system with isolated singularity

Zhijie Chen, Chang-Shou Lin

arXiv preprint

2014

A new type of non-topological bubbling solutions to a competitive Chern-Simons model

Zhijie Chen, Chang-Shou Lin

arXiv preprint

2013

Multiple sign-changing and semi-nodal solutions for coupled Schrodinger equations

Zhijie Chen, Chang‐Shou Lin, Wenming Zou

arXiv (Cornell University)

DOI

2012

Existence and symmetry of positive ground states for a doubly critical Schrodinger system

Zhijie Chen, Wenming Zou

arXiv (Cornell University)

DOI

2012

Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case

Zhijie Chen, Wenming Zou

arXiv preprint

DOI

2012

Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system

Zhijie Chen, Chang-Shou Lin, Wenming Zou

arXiv preprint

2012

Standing Waves for nonlinear Schrodinger Equations involving critical growth

Jianjun Zhang, Zhijie Chen, Wenming Zou

arXiv preprint

书籍

2014

Solutions of Nonlinear Schrӧdinger Systems

Zhijie Chen

Springer theses

DOI

研究方向

椭圆偏微分方程变分法复变量常微分方程

此主页由公开资料整理，尚未经学者本人认领。

精选作品

期刊论文

Green functions, Hitchin's formula, and curvature equations on tori II: Rectangular torus

Proof of a conjecture of Dahmen and Beukers on counting integral Lamé equations with finite monodromy

Asymptotic profiles of low-energy solutions to repulsive Schrödinger systems with critical exponents

Asymptotic behaviors of least energy solutions for weakly coupled nonlinear Schrödinger systems

Existence of solutions to a strongly coupled system for the curl-curl operator with critical exponent

Concentration phenomena of positive solutions to weakly coupled Schrödinger systems with large exponents in dimension two

Monodromy of a generalized Lamé equation of third order

Existence of solutions to Hamilton systems for the curl–curl operator with subcritical nonlinearities

Sharp estimates and non-degeneracy of low energy nodal solutions for the Lane–Emden equation in dimension two

On the closure of the Airault–Mckean–Moser locus for elliptic KdV potentials via Darboux transformations

Energy quantization of the two dimensional Lane-Emden equation with vanishing potentials

Critical points of the Eisenstein series $E_{4}$ and application to the spectrum of the Lamé operator

Co-Axial Metrics on the Sphere and Algebraic Numbers

Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, II

Asymptotic behavior of least energy nodal solutions for biharmonic Lane–Emden problems in dimension four

On number and evenness of solutions of the $SU(3)$ Toda system on flat tori with non-critical parameters

Sharp upper bound of the number of solutions for the SU(N + 1) Toda system on torus with non-critical parameters

Spectrum of the Lamé operator and application, I: Deformation along Re τ = 1 2

The geometry of generalized Lamé equation, III: One-to-one of the Riemann–Hilbert correspondence

Spectrum of the Lamé Operator and Application, II: When an Endpoint is a Cusp

On Algebro-Geometric Simply-Periodic Solutions of the KdV Hierarchy

The geometry of generalized Lamé equation, II: Existence of pre-modular forms and application

Simple zero property of some holomorphic functions on the moduli space of tori

The geometry of generalized Lamé equation, I

Unitary monodromy implies the smoothness along the real axis for some Painlevé VI equation, I

Standing waves for coupled nonlinear Schrödinger equations with decaying potentials

Standing waves for a coupled system of nonlinear Schrödinger equations

预印本

Sharp weighted Carleman and Huber isoperimetric inequalities on the unit ball in higher dimensions

Qualitative analysis of positive singular solutions for a critical elliptic system in a punctured ball

Liouville theorems and symmetry of positive solutions for partially confined nonlinear Schrödinger equations

Sharp criteria for the existence of solutions to curvature equations with two singular sources on rectangular torus

Exact counting of spherical metrics with one conical singularity on rectangular tori

Geometric analysis on rhombus torus: Green function with two singularities

Uniqueness and nonuniqueness for mean field equations with multiple singularities on flat tori

Structure of critical points of multiple Green functions on flat torus and applications

On the Classification of blow-up solutions of a singular Liouville equation on the disk

Critical points of the Moser-Trudinger functional on conical singular surfaces, I: compactness

Sharp stability on the second Robin eigenvalue with negative boundary parameters

Sovability of curvature equations with multiple singular sources on torus via Painleve VI equations

Generic non-degeneracy of critical points of multiple Green functions on torus and applications to curvature equations

On the distribution of critical points of the Eisenstein series $E_6$ and monodromy interpretation

Monodromy of generalized Lame equations with Darboux-Treibich-Verdier potentials: A universal law

Sharp estimates, uniqueness and nondegeneracy of positive solutions of the Lane-Emden system in planar domains

Asymptotic behavior of positive solutions to the Lane-Emden system in dimension two

Modular Ordinary Differential Equations on ${\rm SL}(2,\mathbb{Z})$ of Third Order and Applications

A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in $\mathbb{R}$

Sharp nonexistence results for curvature equations with four singular sources on rectangular tori

Critical points of the classical Eisenstein series of weight two

On reducible monodromy representations of some generalized Lamé equation

Non-existence of solutions for a mean field equation on flat tori at critical parameter $16π$

Real-root property of the spectral polynomial of the Treibich-Verdier potential and related problems

Hamiltonian system for the elliptic form of Painlevé VI equation

Removable singularity of positive solutions for a critical elliptic system with isolated singularity

A new type of non-topological bubbling solutions to a competitive Chern-Simons model

Multiple sign-changing and semi-nodal solutions for coupled Schrodinger equations

Existence and symmetry of positive ground states for a doubly critical Schrodinger system

Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case

Infinitely many sign-changing and semi-nodal solutions for a nonlinear Schrodinger system

Standing Waves for nonlinear Schrodinger Equations involving critical growth

书籍

Solutions of Nonlinear Schrӧdinger Systems

研究方向

Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case