丁彦恒

中国科学院数学与系统科学研究院

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  • 丁彦恒
  • 研究员
  • 南楼 822

个人简况:

丁彦恒 男,四川人,研究员
1989—1991 中科院数学所博士后
1996—1998 德国洪堡学者
2008—2013 意大利国际理论物理中心高级客座学者
办公室:思源楼522 电话:010-62651299 电邮:dingyh@math.ac.cn
研究方向:

非线性泛函分析,变分方法,Hamilton 力学,偏微分方程    

代表著作:

Ding, Yanheng: Variational methods for strongly indefinite problems.Interdisciplinary Mathematical Sciences, 7. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2007.
论文:
 [109]  Ding, Yanheng; Li, Jiongyue;Xu, Tian: Bifurcation on compact spin manifold. Calc. Var. Partial Differential Equations 55 (2016), no. 4, Paper No. 90, 17 pp.  
[108] Ding, Yanheng; Ruf, Bernhard:  On multiplicity of semi-classical solutions to a nonlinear Maxwell-Dirac system. J. Differential Equations 260 (2016), no. 7, 5565–5588.  
[107]  Ding, Yanheng; Xu, Tian:  Concentrating patterns of reaction--diffusion systems:  A variational approach.  Trans. Amer. Math. Soc., 360 (2017), no. 1, 97--138.
[106]  Ding, Yanheng; Liu, Xiaoying:  Periodic solutions of a Dirac equation with concave and convex nonlinearities.  J. Differential Equations 258 (2015), no. 10, 3567--3588.
[105] Ding, Yanheng; Xu, Tian: Localized Concentration of Semi-Classical States for Nonlinear Dirac Equations, Arch. Rational Mech. Anal.  216  (2015),  no. 2,  415--447
[104] Ding, Yanheng; Lee, Cheng; Zhao, Fukun: Semiclassical limits of ground state solutions to Schrödinger systems Calc. Var. Partial Differential Equations, 51 (2014), 725–760.
[103] Ding, Yanheng; Xu, Tian On semi-classical limits of ground states of a nonlinear Maxwell-Dirac system. Calc. Var. Partial Differential Equations 51 (2014), no. 1-2, 17–44.
[102] Ding, Yanheng; Liu, Xiaoying Periodic waves of nonlinear Dirac equations. Nonlinear Anal. 109 (2014), 252–267.
[101] Yang, Minbo; Wei, Yuanhong; Ding, Yanheng Existence of semiclassical states for a coupled Schrödinger system with potentials and nonlocal nonlinearities. Z. Angew. Math. Phys. 65 (2014), no. 1, 41–68.
[100] Ding, Yanheng; Xu, Tian On the concentration of semi-classical states for a nonlinear Dirac-Klein-Gordon system. J. Differential Equations 256 (2014), no. 3, 1264–1294.
[99] Ding, Yanheng; Wei, Juncheng; Xu, Tian Existence and concentration of semi-classical solutions for a nonlinear Maxwell-Dirac system. J. Math. Phys. 54 (2013), no. 6, 061505, 33 pp.
[98] Ding, Yanheng; Lee, Cheng; Ruf, Bernhard: On semiclassical states of a nonlinear Dirac equation. Proc. Roy. Soc. Edinburgh Sect. A 143 (2013), no. 4, 765–790.
[97] Yang, Minbo; Ding, Yanheng Existence of solutions for singularly perturbed Schrödinger equations with nonlocal part. Commun. Pure Appl. Anal. 12 (2013), no. 2, 771–783.
[96] Yang, Minbo; Ding, Yanheng Existence and multiplicity of semiclassical states for a quasilinear Schrödinger equation in R^N. Commun. Pure Appl. Anal. 12 (2013), no. 1, 429–449.
[95] Ding, Yanheng; Ruf, Bernhard Existence and concentration of semiclassical solutions for Dirac equations with critical nonlinearities. SIAM J. Math. Anal. 44 (2012), no. 6, 3755–3785.
[94] Yang, Minbo; Zhao, Fukun; Ding, Yanheng On the existence of solutions for Schrödinger-Maxwell systems in R^3. Rocky Mountain J. Math. 42 (2012), no. 5, 1655–1674.
[93] Ding, Yanheng; Liu, Xiaoying On semiclassical ground states of a nonlinear Dirac equation. Rev. Math. Phys. 24 (2012), no. 10, 1250029, 25 pp.
[92] Yang, Minbo; Ding, Yanheng Stationary states for nonlinear Dirac equations with superlinear nonlinearities. Topol. Methods Nonlinear Anal. 39 (2012), no. 1, 175–188.
[91] Ding, Yanheng; Liu, Xiaoying Semi-classical limits of ground states of a nonlinear Dirac equation. J. Differential Equations 252 (2012), no. 9, 4962–4987
[90] Yang, Minbo; Ding, Yanheng Existence of semiclassical states for a quasilinear Schrödinger equation with critical exponent in R^N. Ann. Mat. Pura Appl. (4) 192 (2013),  783–804.
[89] Ding, Yanheng; Liu, Xiaoying Semiclassical solutions of Schrödinger equations with magnetic fields and critical nonlinearities. Manuscripta Math. 140 (2013), no. 1-2, 51–82.
[88] Ding, Yanheng; Wang, Zhi-Qiang: Bound states of nonlinear Schrödinger equations with magnetic fields. Annali di Matematica Pura ed Applicata, 190 (2011), no. 3, 427-451
[87] Chen, Wenxiong; Yang, Minbo; Ding, Yanheng: Homoclinic orbits of first order discrete Hamiltonian systems with super linear terms. SCIENCE CHINA Mathematics, 54 (2011), no. 12,2583-2596
[86] Ding, Yan Heng Variational methods for strongly indefinite problems. (Chinese) Acta Anal. Funct. Appl. 13 (2011), no. 2,209–217,
[85] Zhao, Fukun; Zhao, Leiga; Ding, Yanheng Multiple solutions for a superlinear and periodic elliptic system on . Z. Angew. Math. Phys.62 (2011), no. 3, 495–511
[84] Yang, Minbo; Shen, Zifei; Ding, Yanheng On a class of infinite-dimensional Hamiltonian systems with asymptotically periodic nonlinearities. Chin. Ann. Math. Ser. B 32 (2011), no. 1, 45–58,
[83] Zhao, Fukun; Ding, Yanheng On Hamiltonian elliptic systems with periodic or non-periodic potentials. J. Differential Equations 249 (2010), no. 12, 2964–2985.
[82] Ding, Yanheng Semi-classical ground states concentrating on the nonlinear potential for a Dirac equation. J. Differential Equations 249 (2010), no. 5, 1015–1034,
[81] Yang, Minbo; Chen, Wenxiong; Ding, Yanheng Solutions for discrete periodic Schrödinger equations with spectrum 0. Acta Appl.Math. 110 (2010), no. 3, 1475–1488,
[80] Yang, Minbo; Zhao, Fukun; Ding, Yanheng Infinitely many stationary solutions of discrete vector nonlinear Schrödinger equation with symmetry. Appl. Math. Comput. 215 (2010), no. 12, 4230–4238,
[79] Zhao, Fukun; Zhao, Leiga; Ding, Yanheng Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems. ESAIM Control Optim. Calc. Var. 16 (2010), no. 1, 77–91,
[78] Yang, Minbo; Chen, Wenxiong; Ding, Yanheng Solutions for periodic Schrödinger equation with spectrum zero and general superlinear nonlinearities. J. Math. Anal. Appl. 364 (2010), no. 2, 404–413
[77] Yang, Minbo; Chen, Wenxiong; Ding, Yanheng Solutions of a class of Hamiltonian elliptic systems in R^n. J. Math. Anal. Appl. 362 (2010), no. 2, 338–349
[76] Zhao, Fukun; Zhao, Leiga; Ding, Yanheng A note on superlinear Hamiltonian elliptic systems. J. Math. Phys. 50 (2009), no. 11, 112702, 7 pp
[75] Ding, Yanheng; Lee, Cheng Homoclinics for asymptotically quadratic and superquadratic Hamiltonian systems. Nonlinear Anal. 71 (2009), no. 5-6, 1395–1413.
[74] Yang, Minbo; Shen, Zifei; Ding, Yanheng Multiple semiclassical solutions for the nonlinear Maxwell-Schrödinger system. Nonlinear Anal. 71 (2009), no. 3-4, 730–739,
[73] Ding, Yanheng; Lee, Cheng Existence and exponential decay of homoclinics in a nonperiodic superquadratic Hamiltonian system. J. Differential Equations 246 (2009), no. 7, 2829–2848.
[72] Zhao, Fukun; Ding, Yanheng Infinitely many solutions for a class of nonlinear Dirac equations without symmetry. Nonlinear Anal. 70 (2009), no. 2, 921–935,
[71] Zhao, Fukun; Ding, Yanheng On a diffusion system with bounded potential. Discrete Contin. Dyn. Syst. 23 (2009), no. 3,1073–1086,
[70] Zhao, Fukun; Zhao, Leiga; Ding, Yanheng Multiple solutions for asymptotically linear elliptic systems. NoDEA Nonlinear Differential Equations Appl. 15 (2008), no. 6, 673–688.
[69] Zhao, Fukun; Zhao, Leiga; Ding, Yanheng: Existence and multiplicity of solutions for a non-periodic Schrödinger equation. Nonlinear Anal. 69 (2008), no. 11, 3671–3678.
[68] Yanheng Ding; Juncheng Wei: Stationary states of nonlinear Dirac equations with general potentials, Reviews in Mathematical Physics, 20 (2008),1007--1032
[67] Yanheng Ding; Bernhard Ruf: Solutions of a nonlinear Dirac equation with external fields, Arch. Rational Mech. Anal. 190 (2008),57--82
[66] Fukun Zhao; Yanheng Ding: Infinitely many solutions for a class of nonlinear Dirac equations without symmetry, Nonlinear Analysis, In press, doi: 10.1016/j.na.2008.01.023
[65] Fukun Zhao; Leiga Zhao; Yanheng Ding: Existence and multiplicity of solutions for a non-periodic Schrodinger equation, Nonlinear Analysis , In press, doi: 10.1016/j.na.2007.10.024
[64] Ding, Yanheng; Wei, Juncheng: Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials. J. Funct. Anal. 251 (2007), no. 2, 546--572.
[63] Ding, Yanheng; Luan, Shixia; Willem, Michel Solutions of a system of diffusion equations. J. Fixed Point Theory Appl. 2 (2007), no. 1, 117--139.
[62] Alves, Claudianor O.; Ding, Yanheng: Existence, multiplicity and concentration of positive solutions for a class of quasilinear problems. Topol. Methods Nonlinear Anal. 29 (2007), no. 2, 265--278.
[61] Ding, Yanheng; Lin, Fanghua Solutions of perturbed Schrödinger equations with critical nonlinearity. Calc. Var. Partial Differential Equations 30 (2007), no. 2, 231—249
[60] Ding, Yanheng; Jeanjean, Louis Homoclinic orbits for a nonperiodic Hamiltonian system. J. Differential Equations 237 (2007), no. 2, 473--490.
[59] Ding, Yanheng; Szulkin, Andrzej Bound states for semilinear Schrödinger equations with sign-changing potential. Calc. Var. Partial Differential Equations 29 (2007), no. 3, 397--419.
[58] Mao, Anmin; Luan, Shixia; Ding, Yanheng Periodic solutions for a class of first order super-quadratic Hamiltonian system. J. Math. Anal.Appl. 330 (2007), no. 1, 584--596.
[57] Ding, Yanheng Multiple homoclinics in a Hamiltonian system with asymptotically or super linear terms. Commun. Contemp. Math. 8 (2006), no. 4, 453--480.
[56] Bartsch, Thomas; Ding, Yanheng Deformation theorems on non-metrizable vector spaces and applications to critical point theory.Math. Nachr. 279 (2006), no. 12, 1267--1288.
[55] Ding, Yanheng; Lin, Fanghua Semiclassical states of Hamiltonian system of Schrödinger equations with subcritical and critical nonlinearities. J. Partial Differential Equations 19 (2006), no. 3,232--255.
[54] Bartsch, Thomas; Ding, Yanheng Solutions of nonlinear Dirac equations. J. Differential Equations 226 (2006), no. 1, 210--249.
[53] Ding, Yanheng; Lee, Cheng Multiple solutions of Schrödinger equations with indefinite linear part and super or asymptotically linear terms. J. Differential Equations 222 (2006), no. 1, 137--163.
[52] Ding, Yanheng; Szulkin, Andrzej Existence and number of solutions for a class of semilinear Schrödinger equations. Contributions to nonlinear analysis, 221--231, Progr. Nonlinear Differential Equations Appl., 66, Birkhäuser, Basel, 2006
[51] Ding, Yanheng; Lee, Cheng Periodic solutions of an infinite dimensional Hamiltonian system. Rocky Mountain J. Math. 35 (2005),no. 6, 1881--1908.
[50] Li, Chong; Ding, Yanheng; Li, Shujie Multiple solutions of nonlinear elliptic equations for oscillation problems. J. Math. Anal.Appl. 303 (2005), no. 2, 477--485.
[49] Ding, Yanheng Deformation in locally convex topological linear spaces. Sci. China Ser. A 47 (2004), no. 5, 687--710.
[48] Clapp, Mónica; Ding, Yanheng; Hernández-Linares, Sergio Strongly indefinite functionals with perturbed symmetries and multiple solutions of nonsymmetric elliptic systems. Electron. J. Differential Equations 2004, No. 100, 18 pp.
[47] Clapp, Mónica; Ding, Yanheng Positive solutions of a Schrödinger equation with critical nonlinearity. Z. Angew. Math. Phys. 55 (2004), no. 4, 592--605.
[46] Ding, Yanheng; Luan, Shixia Multiple solutions for a class of nonlinear Schrödinger equations. J. Differential Equations 207 (2004), no. 2, 423--457.
[45] Mao, Anmin; Luan, Shixia; Ding, Yanheng On the existence of positive solutions for a class of singular boundary value problems. J. Math. Anal. Appl. 298 (2004), no. 1, 57--72.
[44] Ding, Yanheng Homoclinic orbits of Hamiltonian systems. Morse theory, minimax theory and their applications to nonlinear differential equations, 57--65, New Stud. Adv. Math., 1, Int. Press, Somerville, MA, 2003.
[43] Ding, Yanheng; Tanaka, Kazunaga Multiplicity of positive solutions of a nonlinear Schrödinger equation. Manuscripta Math. 112 (2003), no. 1, 109--135.
[42] Clapp, Mónica; Ding, Yanheng Minimal nodal solutions of a Schrödinger equation with critical nonlinearity and symmetric potential. Differential Integral Equations 16 (2003), no. 8, 981--992.
[41] De Figueiredo, D. G.; Ding, Y. H. Strongly indefinite functional and multiple solutions of elliptic systems. Trans. Amer. Math. Soc. 355 (2003), no. 7, 2973--2989
[40] Alves, C. O.; Ding, Y. H. Multiplicity of positive solutions to a p-Laplacian equation involving critical nonlinearity. J. Math. Anal. Appl. 279 (2003), no. 2, 508--521.
[39] Bartsch, Thomas; Ding, Yanheng Homoclinic solutions of an infinite-dimensional Hamiltonian system. Math. Z. 240 (2002), no. 2, 289--310.
[38] deFigueiredo, D. G.; Ding, Y. H. Solutions of a nonlinear Schrödinger equation. Discrete Contin. Dyn. Syst. 8 (2002), no. 3,563--584.
[37] Ding, Yanheng Solutions to a class of Schrödinger equations. Proc. Amer. Math. Soc. 130 (2002), no. 3, 689—696
[36] Bartsch, Thomas; Ding, Yanheng Periodic solutions of superlinear beam and membrane equations with perturbations from symmetry. Nonlinear Anal. 44 (2001), no. 6, Ser. A: Theory Methods, 727--748.
[35] Ding, Yanheng; Lee, Cheng Periodic solutions of Hamiltonian systems. SIAM J. Math. Anal. 32 (2000), no. 3, 555—571
[34] Bartsch, T.; Ding, Y. H. Critical-point theory with applications to asymptotically linear wave and beam equations. Differential Integral Equations 13 (2000), no. 7-9, 973--1000.
[33] Ding, Yanheng; Willem, Michel Homoclinic orbits of a Hamiltonian system. Z. Angew. Math. Phys. 50 (1999), no. 5, 759--778.
[32] Ding, Yanheng; Girardi, Mario Infinitely many homoclinic orbits of a Hamiltonian system with symmetry. Nonlinear Anal. 38 (1999), no. 3, Ser. A: Theory Methods, 391--415.
[31] Bartsch, T.; Ding, Y. H.; Lee, C. Periodic solutions of a wave equation with concave and convex nonlinearities. J. Differential Equations 153 (1999), no. 1, 121--141.
[30] Bartsch, Thomas; Ding, Yanheng On a nonlinear Schrödinger equation with periodic potential. Math. Ann. 313 (1999), no. 1,15--37.
[29] Ding, Yanheng Infinitely many homoclinic orbits for a class of Hamiltonian systems with symmetry. A Chinese summary appears in Chinese Ann. Math. Ser. A 19 (1998), no. 2, 283. Chinese Ann. Math.Ser. B 19 (1998), no. 2, 167--178.
[28] Ding, Yanheng; Li, Shujie; Willem, Michel Periodic solutions of symmetric wave equations. J. Differential Equations 145 (1998), no. 2,217--241.
[27] Ding, Yanheng Infinitely many entire solutions of an elliptic system with symmetry. Topol. Methods Nonlinear Anal. 9 (1997), no. 2, 313--323.
[26] Ding, Yanheng; Li, Shujie Periodic solutions of a superlinear wave equation. Nonlinear Anal. 29 (1997), no. 3, 265--282.
[25] Ding, Yanheng; Girardi, M. Periodic solutions for a class of symmetric and subquadratic Hamiltonian systems. Math. Comput. Modelling 23 (1996), no. 7, 59--71.
[24] Ding, Yanheng; Li, Shujie Existence of entire solutions of an elliptic equation on $R\sp N$. Functional analysis in China, 277--299, Math. Appl., 356, Kluwer Acad. Publ., Dordrecht, 1996.
[23] Ding, Yanheng; Li, Shujie The existence of infinitely many periodic solutions to Hamiltonian systems in a symmetric potential well. Ricerche Mat. 44 (1995), no. 1, 163--172.
[22] Ding, Y. H.; Girardi, M. Periodic solutions for a second order Hamiltonian system. Dynamical systems and applications, 229--237, World Sci. Ser. Appl. Anal., 4, World Sci. Publ., River Edge, NJ, 1995.
[21] Ding, Yan Heng Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems. Nonlinear Anal. 25 (1995),no. 11, 1095--1113.
[20] Ding, Yan Heng; Li, Shu Jie Some existence results of solutions for the semilinear elliptic equations on $R\sp N$. J. Differential Equations 119 (1995), no. 2, 401--425.
[19] Ding, Yan Heng; Li, Shu Jie Homoclinic orbits for first order Hamiltonian systems. J. Math. Anal. Appl. 189 (1995), no. 2, 585--601.
[18] Ding, Yan Heng; Li, Shu Jie Existence of entire solutions for some elliptic systems. Bull. Austral. Math. Soc. 50 (1994), no. 3, 501--519.
[17] Ding, Yan Heng A remark on the linking theorem with applications. Nonlinear Anal. 22 (1994), no. 2, 237--250.
[16] Ding, Yan Heng Numerical quadrature and extrapolation for finite elements. (Chinese) J. Systems Sci. Math. Sci. 13 (1993), no. 2, 178--184.
[15] Ding, Yan Heng; Li, Shu Jie Periodic solutions of a class of Hamiltonian systems with singular potentials. Northeast. Math. J. 9 (1993), no. 1, 91--98.
[14] Ding, Yan Heng; Li, Shu Jie Existence of infinitely many periodic solutions to Hamiltonian systems in a potential well. (Chinese) Acta Math. Sinica 36 (1993), no. 1, 25--30.
[13] Yanheng, Ding; Girardi, Mario Periodic and homoclinic solutions to a class of Hamiltonian systems with the potentials changing sign. Dynam. Systems Appl. 2 (1993), no. 1, 131--145.
[12] Ding, Yan Heng; Li, Shu Jie Two results on periodic solutions of singular Hamiltonian systems. Lecture notes in contemporary mathematics. Vol. 2, 1991, 84--93, Science Press, Beijing, 1992.
[11] Ding, Yan Heng; Lin, Qun Quadrature and finite element error expansions on isoparametric quadrilateral meshes. (Chinese) Acta Math. Appl. Sinica 15 (1992), no. 4, 530--540.
[10] Ding, Yan Heng Some existence results on homoclinics for a class of second order conservative systems. Ann. Univ. Ferrara Sez. VII (N.S.) 38 (1992), 49--63 (1993).
[9] Ding, Yan Heng; Li, Shu Jie Periodic solutions of some singulardynamical systems in a potential well. Chinese J. Contemp. Math. 13 (1992), no. 4, 299--307 (1993).
[8] Ding, Yan Heng; Li, Shu Jie Periodic solutions to singular dynamical systems on a potential well. (Chinese) Chinese Ann. Math. Ser. A 13 (1992), no. 5, 546--554.
[7] Ding, Yan Heng; Li, Shu Jie A remark on periodic solutions of singular Hamiltonian systems with sublinear terms. Systems Sci. Math. Sci. 5 (1992), no. 2, 121--126.
[6] Ding, Yan Heng; Lin, Qun Finite element error expansions for the eigenvalue approximation to the multigroup diffusion equations. Systems Sci. Math. Sci. 4 (1991), no. 3, 225--235.
[5] Ding, Yan Heng; Lin, Qun Quadrature and extrapolation for the variable coefficient elliptic eigenvalue problem. Systems Sci. Math. Sci. 3 (1990), no. 4, 327--336.
[4] Ding, Yan Heng A note on nonlinear beam equations. (Chinese) Acta Math. Sinica 33 (1990), no. 2, 172--181.
[3] Ding, Yan Heng; Lin, Qun Finite element expansion for variable coefficient elliptic problems. Systems Sci. Math. Sci. 2 (1989), no. 1, 54--69.
[2] Ding, Yan Heng; Liu, Jia Quan Periodic solutions of asymptotically linear Hamiltonian systems. (Chinese) J. Systems Sci. Math. Sci. 9 (1989), no. 1, 30--39.
[1] Ding, Yan Heng Nonlinear vibrations in the n-dimensional beam equation. (Chinese) J. Systems Sci. Math. Sci. 8 (1988), no. 1, 42--45.