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 Schr��dinger 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, 第 11 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, 第 11 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 Schr��dinger 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, 第 11 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 Schr��dinger 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, 第 11 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 Schr��dinger 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, 第 11 作者
(29) Semiclassical limits of ground state solutions to Schr��dinger systems, Calculus of Variations and Partial Differential Equations,, 2014, 第 1 作者
(30) Existence of solutions for singularly perturbed Schr��dinger equations with nonlocal part., Commun. Pure Appl. Anal., 2013, 第 1 作者
(31) Existence and multiplicity of semiclassical states for a quasilinear Schr��dinger equation in RN., Commun. Pure Appl. Anal., 2013, 第 1 作者
(32) Existence of semiclassical states for a quasilinear Schr��dinger equation with critical exponent in RN., Ann. Mat. Pura Appl, 2013, 第 1 作者
(33) Existence of semiclassical states for a quasilinear Schr��dinger equation with critical exponent in $${\mathbb{R}^N}$$, Annali di Matematica Pura ed Applicata,, 2013, 第 2 作者
(34) Semiclassical solutions of Schr��dinger 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, 第 11 作者
(36) EXISTENCE AND CONCENTRATION OF SEMICLASSICAL SOLUTIONS FOR DIRAC EQUATIONS WITH CRITICAL NONLINEARITIES, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2012, 第 11 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, 第 11 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, 第 11 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, 第 11 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, 第 11 作者
(47) STATIONARY STATES OF NONLINEAR DIRAC EQUATIONS WITH GENERAL POTENTIALS, REVIEWS IN MATHEMATICAL PHYSICS, 2008, 第 11 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, 第 11 作者
(50) Semiclassical states for nonlinear Schr��dinger 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, 第 11 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 Schr��dinger 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 Schr��dinger equations, Journal of Differential Equations, 2004, 第 1 作者
(59) Multiplicity of positive solutions of a nonlinear Schr��dinger 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 ) 现代变分理论的若干前沿课题, 参与, 国家任务, 2021-01--2025-12
( 2 ) 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
( 3 ) 变分方法与Dirac系统, 参与, 国家任务, 2016-02--2019-12
( 4 ) 现代变分理论的若干问题研究, 负责人, 国家任务, 2014-01--2018-12
( 5 ) 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