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招生专业 070101-基础数学 招生方向 (非线性)泛函分析 教授课程 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 科研项目 ( 1 ) 非线性变分理论的若干前沿课题, 主持, 国家级, 2009-01--2012-12 ( 2 ) 现代变分理论的若干问题研究, 主持, 国家级, 2014-01--2018-12 ( 3 ) 变分方法与Dirac系统, 参与, 国家级, 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, 国家级, 2019-02--2023-01

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(1) Multiplicity and concentration for Kirchhoff type equations around topologically critical points in potential, Topol. Methods Nonlinear Anal., 2019, 第 2 作者 (2) Existence and Concentration for Kirchhoff Type Equations around Topologically Critical Points of the Potential, Topol. Methods Nonlinear Anal., 2019, 第 1 作者 (3) Homoclinic solutions for an anomalous diffusion system, J. Math. Anal. Appl., 2018, 第 1 作者 (4) Periodic solutions of an asymptotically linear Dirac equation., Ann. Mat. Pura Appl. (4), 2017, 第 1 作者 (5) Multiplicity of semiclassical solutions to nonlinear Schrödinger equations., J. Fixed Point Theory Appl. 19 (2017), no. 1,, 2017, 第 1 作者 (6) 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 (7) 强不定问题的变分方法, 中国科学, 2017, 第 1 作者 (8) Bifurcation on compact spin manifold, Calc. Var. Partial Differential Equations, 2016, 第 1 作者 (9) On multiplicity of semi-classical solutions to a nonlinear Maxwell-Dirac system., J. Differential Equations, 2016, 第 1 作者 (10) CONCENTRATING PATTERNS OF REACTION-DIFFUSION, Trans. Amer. Math. Soc., 2016, 第 1 作者 (11) Periodic solutions of a Dirac equation with concave and convex nonlinearities, J. Differential Equations, 2015, 第 1 作者 (12) Localized concentration of semi-classical states for nonlinear Dirac equations, Arch. Ration. Mech. Anal., 2015, 第 1 作者 (13) Semiclassical limits of ground state solutions to Schrödinger systems, Calc. Var. Partial Differential Equations, 2014, 第 1 作者 (14) On semi-classical limits of ground states of a nonlinear Maxwell-Dirac system., Calc. Var. Partial Differential Equations, 2014, 第 1 作者 (15) Periodic waves of nonlinear Dirac equations., Nonlinear Anal, 2014, 第 1 作者 (16) Existence of semiclassical states for a coupled Schrödinger system with potentials and nonlocal nonlinearities., Z. Angew. Math. Phys., 2014, 第 3 作者 (17) On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system., J. Differential Equations, 2014, 第 1 作者 (18) On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system., J. Differential Equations, 2014, 第 1 作者 (19) Existence of semiclassical states for a quasilinear Schrödinger equation with critical exponent in RN., Ann. Mat. Pura Appl, 2013, 第 2 作者 (20) Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities, Manuscripta Math., 2013, 第 1 作者 (21) Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part., Commun. Pure Appl. Anal., 2013, 第 2 作者 (22) Existence and multiplicity of semiclassical states for a quasilinear Schrödinger equation in RN., Commun. Pure Appl. Anal., 2013, 第 2 作者 (23) Semi-classical limits of ground states of a nonlinear Dirac equation , J. Differential Equations, 2012, 第 1 作者 (24) Existence and concentration of semiclassical solutions for Dirac equations with critical nonlinearities., SIAM J. Math. Anal., 2012, 第 1 作者 (25) On semiclassical ground states of a nonlinear Dirac equation., Rev. Math. Phys., 2012, 第 1 作者 (26) Stationary states for nonlinear Dirac equations with superlinear nonlinearities., Topol. Methods Nonlinear Anal., 2012, 第 2 作者 (27) Semiclassical solutions of Schr?dinger equations with magnetic fields and critical nonlinearities , Manuscripta Mathematica, 2012, 第 1 作者 (28) Existence of semiclassical states for a quasilinear Schr?dinger equation with critical exponent in R^N, Annali di Matematica, 2012, 第 2 作者 (29) 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 (30) 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 (31) Homoclinic orbits of first order discrete Hamiltonian systems with super linear terms, SCIENCE CHINA Mathematics, 2011, 第 3 作者 (32) 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 (33) 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 (34) A note on superlinear Hamiltonian elliptic systems, A note on superlinear Hamiltonian elliptic systems, J. Math. Phys, 2009, 第 3 作者 (35) 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 (36) 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 (37) 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 (38) 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 (39) 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 (40) Homoclinic orbits for a nonperiodic Hamiltonian system. , Homoclinic orbits for a nonperiodic Hamiltonian system. , J. Differential Equations , 2007, 第 1 作者 (41) 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 (42) 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 (43) 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 (44) Solutions of nonlinear Dirac equations., Solutions of nonlinear Dirac equations., J. Differential Equations , 2006, 第 2 作者 (45) 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 (46) Deformation in locally convex topological linear spaces. , Deformation in locally convex topological linear spaces. , Sci. China Ser. A, 2004, 第 1 作者 (47) 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 (48) 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 (49) 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 (50) 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 (51) Homoclinic solutions of an infinite-dimensional Hamiltonian system., Homoclinic solutions of an infinite-dimensional Hamiltonian system., Math. Z. , 2002, 第 2 作者 (52) 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 (53) Periodic solutions of Hamiltonian systems, Periodic solutions of Hamiltonian systems, SIAM J. Math. Anal. , 2000, 第 1 作者 (54) Homoclinic orbits of a Hamiltonian system, Homoclinic orbits of a Hamiltonian system, Z. Angew. Math. Phys., 1999, 第 1 作者 (55) 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 (56) 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 (57) Periodic solutions of symmetric wave equations., Periodic solutions of symmetric wave equations., J. Differential Equations , 1998, 第 1 作者 (58) 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 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

学术兼职

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

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