基本信息
丁彦恒  男  博导  中国科学院数学与系统科学研究院
电子邮件: dingyh@math.ac.cn
通信地址: 中关村东路55号中科院数学院
邮政编码: 100190

招生信息

   
招生专业
070101-基础数学
招生方向
(非线性)泛函分析

工作经历

   
社会兼职
2016-07-31-今,中国数学会非线性泛函分析专业委员会, 副理事长

教授课程

微积分 I A
微积分 II-III A
数学分析
微积分I-A
微积分Ⅱ-B
微积分I-B
微积分III-B
变分方法及其应用

专利与奖励

   
奖励信息
(1) 2022年北京高校优质本科教材课件, 部委级, 2022
(2) 本科生优秀课程, 研究所(学校), 2020

出版信息

   
发表论文
(1) Normalized solution to the Schrödinger equation with potential and general nonlinear term: Mass super-critical case Yanheng Ding a,b,1 , Xuexiu Zhong, Journal of Differential Equations, 2022, 第 1 作者
(2) Solutions to a nonlinear Dirac–Maxwell system: from periodic waves to soliton-like waves, Nonliearity, 2022, 第 1 作者
(3) Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations, CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 第 1 作者
(4) Infinitely many solutions of Dirac equations with concave and convex nonlinearities, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2021, 通讯作者
(5) Existence of semiclassical solutions for some critical Dirac equation, JOURNAL OF MATHEMATICAL PHYSICS, 2021, 第 1 作者
(6) STATIONARY STATES OF DIRAC--KLEIN--GORDON SYSTEMS, SIAM J. MATH. ANAL. Vol. 53, No. 5, pp. 5731--5755(Society for Industrial and Applied Mathematics), 2021, 第 1 作者
(7) ON MULTIPLICITY OF SEMI-CLASSICAL SOLUTIONS TO NONLINEAR DIRAC EQUATIONS OF SPACE-DIMENSION n, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 通讯作者
(8) POTENTIAL WELL AND MULTIPLICITY OF SOLUTIONS FOR NONLINEAR DIRAC EQUATIONS, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 第 2 作者
(9) Semiclassical states for Choquard type equations with critical growth: critical frequency case, NONLINEARITY, 2020, 第 1 作者
(10) Semiclassical states for Dirac-Klein-Gordon system with critical growth, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 第 1 作者
(11) The concentration behavior of ground state solutions for nonlinear Dirac equation, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 第 1 作者
(12) The concentration behavior of ground state solutions for nonlinear Dirac equation., Nonlinear Analysis, 2020, 第 1 作者
(13) Multiplicity and concentration for Kirchhoff type equations around topologically critical points in potential, TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2019, 第 2 作者
(14) Homoclinic solutions for an anomalous diffusion system, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 第 1 作者
(15) Periodic solutions of an asymptotically linear Dirac equation, ANNALI DI MATEMATICA PURA ED APPLICATA, 2017, 第 1 作者
(16) CONCENTRATING PATTERNS OF REACTION-DIFFUSION SYSTEMS: A VARIATIONAL APPROACH, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 第 1 作者
(17) Multiplicity of semiclassical solutions to nonlinear Schrödinger equations, Journal of Fixed Point Theory and Applications,, 2017, 第 1 作者
(18) 强不定问题的变分方法, 中国科学数学, 2017, 第 1 作者
(19) EXISTENCE AND CONCENTRATION FOR KIRCHHOFF TYPE EQUATIONS AROUND TOPOLOGICALLY CRITICAL POINTS OF THE POTENTIAL, COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2017, 第 2 作者
(20) Bifurcation on compact spin manifold, CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2016, 通讯作者
(21) On multiplicity of semi-classical solutions to a nonlinear Maxwell–Dirac system, JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 第 1 作者
(22) Periodic solutions of a Dirac equation with concave and convex nonlinearities, JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 第 1 作者
(23) Positive solutions of a class of semilinear equations with absorption and Schrödinger equations, Journal de mathématiques pures et appliquées, 2015, 
(24) Localized Concentration of Semi-Classical States for Nonlinear Dirac Equations, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2015, 通讯作者
(25) On the concentration of semi-classical states for a nonlinear Dirac–Klein–Gordon system, JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 第 1 作者
(26) Existence of semiclassical states for a coupled Schrödinger system with potentials and nonlocal nonlinearities, Zeitschrift, 2014, 第 3 作者
(27) Periodic waves of nonlinear Dirac equations, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 第 1 作者
(28) On semi-classical limits of ground states of a nonlinear Maxwell–Dirac system, CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2014, 通讯作者
(29) Semiclassical limits of ground state solutions to Schrödinger systems, Calculus of Variations and Partial Differential Equations,, 2014, 第 1 作者
(30) Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part., Commun. Pure Appl. Anal., 2013, 第 1 作者
(31) Existence and multiplicity of semiclassical states for a quasilinear Schrödinger equation in RN., Commun. Pure Appl. Anal., 2013, 第 1 作者
(32) Existence of semiclassical states for a quasilinear Schrödinger equation with critical exponent in RN., Ann. Mat. Pura Appl, 2013, 第 1 作者
(33) Existence of semiclassical states for a quasilinear Schrödinger equation with critical exponent in $${\mathbb{R}^N}$$, Annali di Matematica Pura ed Applicata,, 2013, 第 2 作者
(34) Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities, Manuscripta Mathematica,, 2013, 第 1 作者
(35) ON SEMICLASSICAL GROUND STATES OF A NONLINEAR DIRAC EQUATION, REVIEWS IN MATHEMATICAL PHYSICS, 2012, 通讯作者
(36) EXISTENCE AND CONCENTRATION OF SEMICLASSICAL SOLUTIONS FOR DIRAC EQUATIONS WITH CRITICAL NONLINEARITIES, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 通讯作者
(37) Stationary states for nonlinear Dirac equations with superlinear nonlinearities, TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2012, 第 2 作者
(38) Semi-classical limits of ground states of a nonlinear Dirac equation, JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 通讯作者
(39) Multiple solutions for a superlinear and periodic elliptic system on \mathbbRNR, Zeitschrift für Angewandte Mathematik und Physik, 2011, 第 1 作者
(40) Homoclinic orbits of first order discrete Hamiltonian systems with super linear terms, SCIENCE CHINA-MATHEMATICS, 2011, 第 3 作者
(41) Bound states of nonlinear Schr?dinger equations with magnetic fields, Annali di Matematica Pura ed Applicata, 2011, 第 1 作者
(42) Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation, JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 通讯作者
(43) On Hamiltonian elliptic systems with periodic or non-periodic potentials, JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 第 2 作者
(44) Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system, JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 通讯作者
(45) A note on superlinear Hamiltonian elliptic systems, JOURNAL OF MATHEMATICAL PHYSICS, 2009, 第 3 作者
(46) Solutions of a Nonlinear Dirac Equation with External Fields, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2008, 通讯作者
(47) STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS, REVIEWS IN MATHEMATICAL PHYSICS, 2008, 通讯作者
(48) Solutions of perturbed Schr?dinger equations with critical nonlinearity., Calc. Var. Partial Differential Equations, 2007, 第 1 作者
(49) Homoclinic orbits for a nonperiodic Hamiltonian system, JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 通讯作者
(50) Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials, Journal of Functional Analysis, 2007, 第 1 作者
(51) Bound states for semilinear Schr?dinger equations with sign-changing potential., 2007, 第 1 作者
(52) MULTIPLE HOMOCLINICS IN A HAMILTONIAN SYSTEM WITH ASYMPTOTICALLY OR SUPER LINEAR TERMS, COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2006, 通讯作者
(53) Deformation theorems on non-metrizable vector spaces and applications to critical point theory, MATHEMATISCHE NACHRICHTEN, 2006, 第 2 作者
(54) Solutions of nonlinear Dirac equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 第 2 作者
(55) Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms, Journal of Differential Equations, 2006, 第 1 作者
(56) Positive solutions of a Schr?dinger equation with critical nonlinearity., 2004, 第 1 作者
(57) Deformation in locally convex topological linear spaces, SCIENCE IN CHINA SERIES A-MATHEMATICS, 2004, 
(58) Multiple solutions for a class of nonlinear Schrödinger equations, Journal of Differential Equations, 2004, 第 1 作者
(59) Multiplicity of positive solutions of a nonlinear Schrödinger equation, manuscripta mathematica,, 2003, 第 1 作者
(60) Strongly indefinite functionals and multiple solutions of elliptic systems, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 
(61) Homoclinic solutions of an infinite-dimensional Hamiltonian system, MATHEMATISCHE ZEITSCHRIFT, 2002, 
(62) Periodic solutions of Hamiltonian systems, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2000, 
(63) Homoclinic orbits of a Hamiltonian system, Zeitschrift, 1999, 
(64) Periodic Solutions of a Wave Equation with Concave and Convex Nonlinearities, JOURNAL OF DIFFERENTIAL EQUATIONS, 1999, 
(65) On a nonlinear Schr?dinger equation with periodic potential., 1999, 第 1 作者
(66) Periodic solutions of symmetric wave equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 
(67) Some existence results of solutions for the semilinear elliptic equations on ${\bf R}^N$RN, J. Differential Equations, 1995, 第 1 作者
发表著作
( 1 ) Variational Methods for Strongly Indefinite Problems, Variational Methods for Strongly Indefinite Problems, World Scientific Publishing, 2007-08, 第 1 作者
( 2 ) 数学分析讲义 (第一卷), 科学出版社, 2018-12, 第 1 作者
( 3 ) 数学分析讲义 (第二卷), 科学出版社, 2019-12, 第 1 作者
( 4 ) 数学分析讲义 (第三卷), 科学出版社, 2020-06, 第 1 作者
( 5 ) 数学分析学习指导 (上), 科学出版社, 2021-07, 第 1 作者

科研活动

   
科研项目
( 1 ) 非线性变分理论的若干前沿课题, 负责人, 国家任务, 2009-01--2012-12
( 2 ) 现代变分理论的若干问题研究, 负责人, 国家任务, 2014-01--2018-12
( 3 ) 变分方法与Dirac系统, 参与, 国家任务, 2016-02--2019-12
( 4 ) 强不定变分理论在非线性Dirac方程中的应用, 参与, 国家任务, 2019-02--2023-01
( 5 ) 现代变分理论的若干前沿课题, 参与, 国家任务, 2021-01--2025-12