070101-基础数学

（非线性）泛函分析

   

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

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

   

（1） 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
（2） Nonrelativistic limit and some properties of solutions for nonlinear Dirac equations, Calc. Var. Partial Differential Equations 60 (2021), no. 4, Paper No. 144, 23 pp., 2021, 第 1 作者
（3） On multiplicity of semi-classical solutions to nonlinear Dirac equations of space-dimension n, Discrete Contin. Dyn. Syst. 41 (2021), no. 9, 4105–4123., 2021, 第 1 作者
（4） Infinitely many solutions of Dirac equations with concave and convex nonlinearities, Z. Angew. Math. Phys. 72 (2021), no. 1, Paper No. 39, 17 pp., 2021, 第 1 作者
（5） Existence of semiclassical solutions for some critical Dirac equation, J. Math. Phys. 62 (2021), no. 1, Paper No. 011501, 22 pp., 2021, 第 1 作者
（6） Semiclassical states for Choquard type equations with critical growth: critical frequency case., Nonlinearity, 2020, 第 1 作者
（7） Semiclassical states for Dirac-Klein-Gordon system with critical growth, Journal of Mathematical Analysis and Applications, 2020, 第 1 作者
（8） The concentration behavior of ground state solutions for nonlinear Dirac equation, Nonlinear Anal., 2020, 第 1 作者
（9） Potential well and multiplicity of solutions for nonlinear Dirac equations, Commun. Pure Appl. Anal., 2020, 第 2 作者
（10） Multiplicity and concentration for Kirchhoff type equations around topologically critical points in potential, Topol. Methods Nonlinear Anal., 2019, 第 2 作者
（11） Existence and Concentration for Kirchhoff Type Equations around Topologically Critical Points of the Potential, Topol. Methods Nonlinear Anal., 2019, 第 1 作者
（12） Homoclinic solutions for an anomalous diffusion system, J. Math. Anal. Appl., 2018, 第 1 作者
（13） Periodic solutions of an asymptotically linear Dirac equation., Ann. Mat. Pura Appl. (4), 2017, 第 1 作者
（14） Multiplicity of semiclassical solutions to nonlinear Schrödinger equations., J. Fixed Point Theory Appl. 19 (2017), no. 1,, 2017, 第 1 作者
（15） Existence and concentration for Kirchhoff type equations around topologically critical points of the potential., Commun. Pure Appl. Anal. 16 (2017), no. 5,, 2017, 第 2 作者
（16） 强不定问题的变分方法, 中国科学, 2017, 第 1 作者
（17） Bifurcation on compact spin manifold, Calc. Var. Partial Differential Equations, 2016, 第 1 作者
（18） On multiplicity of semi-classical solutions to a nonlinear Maxwell-Dirac system., J. Differential Equations, 2016, 第 1 作者
（19） CONCENTRATING PATTERNS OF REACTION-DIFFUSION, Trans. Amer. Math. Soc., 2016, 第 1 作者
（20） Periodic solutions of a Dirac equation with concave and convex nonlinearities, J. Differential Equations, 2015, 第 1 作者
（21） Localized concentration of semi-classical states for nonlinear Dirac equations, Arch. Ration. Mech. Anal., 2015, 第 1 作者
（22） Semiclassical limits of ground state solutions to Schrödinger systems, Calc. Var. Partial Differential Equations, 2014, 第 1 作者
（23） On semi-classical limits of ground states of a nonlinear Maxwell-Dirac system., Calc. Var. Partial Differential Equations, 2014, 第 1 作者
（24） Periodic waves of nonlinear Dirac equations., Nonlinear Anal, 2014, 第 1 作者
（25） Existence of semiclassical states for a coupled Schrödinger system with potentials and nonlocal nonlinearities., Z. Angew. Math. Phys., 2014, 第 3 作者
（26） On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system., J. Differential Equations, 2014, 第 1 作者
（27） On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system., J. Differential Equations, 2014, 第 1 作者
（28） Existence of semiclassical states for a quasilinear Schrödinger equation with critical exponent in RN., Ann. Mat. Pura Appl, 2013, 第 2 作者
（29） Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities, Manuscripta Math., 2013, 第 1 作者
（30） Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part., Commun. Pure Appl. Anal., 2013, 第 2 作者
（31） Existence and multiplicity of semiclassical states for a quasilinear Schrödinger equation in RN., Commun. Pure Appl. Anal., 2013, 第 2 作者
（32） Semi-classical limits of ground states of a nonlinear Dirac equation , J. Differential Equations, 2012, 第 1 作者
（33） Existence and concentration of semiclassical solutions for Dirac equations with critical nonlinearities., SIAM J. Math. Anal., 2012, 第 1 作者
（34） On semiclassical ground states of a nonlinear Dirac equation., Rev. Math. Phys., 2012, 第 1 作者
（35） Stationary states for nonlinear Dirac equations with superlinear nonlinearities., Topol. Methods Nonlinear Anal., 2012, 第 2 作者
（36） Semiclassical solutions of Schr？dinger equations with magnetic fields and critical nonlinearities , Manuscripta Mathematica, 2012, 第 1 作者
（37） Existence of semiclassical states for a quasilinear Schr？dinger equation with critical exponent in R^N, Annali di Matematica, 2012, 第 2 作者
（38） Multiple solutions for a superlinear and periodic elliptic system on \mathbbRNR, Multiple solutions for a superlinear and periodic elliptic system on \mathbbRNR, Zeitschrift für Angewandte Mathematik und Physik , 2011, 第 2 作者
（39） Bound states of nonlinear Schr？dinger equations with magnetic fields, Bound states of nonlinear Schr？dinger equations with magnetic fields, Annali di Matematica Pura ed Applicata, 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） On Hamiltonian elliptic systems with periodic or non-periodic potentials. , On Hamiltonian elliptic systems with periodic or non-periodic potentials. , J. Differential Equations , 2010, 第 2 作者
（42） Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation, Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation, J. Differential Equations , 2010, 第 1 作者
（43） A note on superlinear Hamiltonian elliptic systems, A note on superlinear Hamiltonian elliptic systems, J. Math. Phys, 2009, 第 3 作者
（44） Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system, Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system,  J. Differential Equations , 2009, 第 1 作者
（45） Stationary states of nonlinear Dirac equations with general potentials, Stationary states of nonlinear Dirac equations with general potentials, Rev. Math. Phys, 2008, 第 1 作者
（46） Solutions of a nonlinear Dirac equation with external fields., Solutions of a nonlinear Dirac equation with external fields., Arch. Ration. Mech. Anal, 2008, 第 1 作者
（47） Semiclassical states for nonlinear Schr？dinger equations with sign-changing potentials, Semiclassical states for nonlinear Schr？dinger equations with sign-changing potentials, J. Funct. Anal, 2007, 第 1 作者
（48） Solutions of perturbed Schr？dinger equations with critical nonlinearity., 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. , Homoclinic orbits for a nonperiodic Hamiltonian system. , J. Differential Equations , 2007, 第 1 作者
（50） Bound states for semilinear Schr？dinger equations with sign-changing potential. , Bound states for semilinear Schr？dinger equations with sign-changing potential. , Calc. Var. Partial Differential Equations , 2007, 第 1 作者
（51） Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms, Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms, Commun. Contemp. Math., 2006, 第 1 作者
（52） Deformation theorems on non-metrizable vector spaces and applications to critical point theory, Deformation theorems on non-metrizable vector spaces and applications to critical point theory, Math. Nachr., 2006, 第 2 作者
（53） Solutions of nonlinear Dirac equations., Solutions of nonlinear Dirac equations., J. Differential Equations , 2006, 第 2 作者
（54） Multiple solutions of Schr？dinger equations with indefinite linear part and super or asymptotically linear terms. , Multiple solutions of Schr？dinger equations with indefinite linear part and super or asymptotically linear terms. ,  J. Differential Equations, 2006, 第 1 作者
（55） Deformation in locally convex topological linear spaces. , Deformation in locally convex topological linear spaces. , Sci. China Ser. A, 2004, 第 1 作者
（56） Positive solutions of a Schr？dinger equation with critical nonlinearity. , Positive solutions of a Schr？dinger equation with critical nonlinearity. , Z. Angew. Math. Phys, 2004, 第 2 作者
（57） Multiple solutions for a class of nonlinear Schr？dinger equations, Multiple solutions for a class of nonlinear Schr？dinger equations, J. Differential Equations , 2004, 第 1 作者
（58） Multiplicity of positive solutions of a nonlinear Schr？dinger equation., Multiplicity of positive solutions of a nonlinear Schr？dinger equation., Manuscripta Math., 2003, 第 1 作者
（59） Strongly indefinite functionals and multiple solutions of elliptic systems., Strongly indefinite functionals and multiple solutions of elliptic systems.,  Trans. Amer. Math. Soc. , 2003, 第 2 作者
（60） Homoclinic solutions of an infinite-dimensional Hamiltonian system., Homoclinic solutions of an infinite-dimensional Hamiltonian system.,  Math. Z. , 2002, 第 2 作者
（61） Solutions to a class of Schr？dinger equations, Solutions to a class of Schr？dinger equations, Proc. Amer. Math. Soc., 2002, 第 1 作者
（62） Periodic solutions of Hamiltonian systems, Periodic solutions of Hamiltonian systems, SIAM J. Math. Anal. , 2000, 第 1 作者
（63） Homoclinic orbits of a Hamiltonian system, Homoclinic orbits of a Hamiltonian system, Z. Angew. Math. Phys., 1999, 第 1 作者
（64） Periodic solutions of a wave equation with concave and convex nonlinearities., Periodic solutions of a wave equation with concave and convex nonlinearities., J. Differential Equations , 1999, 第 2 作者
（65） On a nonlinear Schr？dinger equation with periodic potential. , On a nonlinear Schr？dinger equation with periodic potential. , Math. Ann., 1999, 第 2 作者
（66） Periodic solutions of symmetric wave equations., Periodic solutions of symmetric wave equations., J. Differential Equations , 1998, 第 1 作者
（67） Some existence results of solutions for the semilinear elliptic equations on ${\bf R}^N$RN, Some existence results of solutions for the semilinear elliptic equations on ${\bf R}^N$RN, J. Differential Equations , 1995, 第 1 作者

（ 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

   

（ 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