丁彥恒

丁彥恒 男，四川人，研究員

1989—1991 中科院數學所博士后

1996—1998 德國洪堡學者

2008—2013 意大利國際理論物理中心高級客座學者

辦公室：思源樓522 電話：010-62651299 電郵：dingyh@math.ac.cn

研究方向：非線性泛函分析，變分方法，Hamilton 力學，偏微分方程

專著：

**Ding, Yanheng: **Variational methods for strongly indefinite problems.Interdisciplinary Mathematical Sciences, 7. *World Scientific Publishing **Co. Pte. Ltd., Hackensack, NJ, *2007.

論文**:**

[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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger-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 Schr?dinger equation with critical exponent in R^N. *Ann. Mat. Pura Appl. (4)* 192 (2013), 783–804.

[89] Ding, Yanheng; Liu, Xiaoying Semiclassical solutions of Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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-Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger equations. *Contributions to nonlinear analysis, *221--231, Progr. Nonlinear Differential Equations Appl., 66, *Birkh?user, 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 Schr?dinger 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 Schr?dinger 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 Schr?dinger equation. *Manuscripta Math. *112 (2003), no. 1, 109--135.

[42] Clapp, Mónica; Ding, Yanheng Minimal nodal solutions of a Schr?dinger 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 Schr?dinger equation. *Discrete Contin. Dyn. Syst. *8 (2002), no. 3,563--584.

[37] Ding, Yanheng Solutions to a class of Schr?dinger 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 Schr?dinger 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.

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聯系電話：86-10-82541600 傳真：86-10-82541591 E-mail：mathlab@math.ac.cn