曹道民

广州大学数学与信息科学学院院长

曹道民，男，湖南常宁人，1963年生，数学家，曾任中国科学院数学与系统科学研究院应用数学研究所所长、研究员、博士生导师。现任广州大学数学与信息科学学院院长。先后在湘潭大学数学系获学士、硕士学位，1989年在中科院武汉数学物理研究所获博士学位。

人物经历

1979年9月至1983年8月湘潭大学数学系基础数学专业学习，获学士学位

1983年9月至1986年7月湘潭大学数学系计算数学专业学习，获硕士学位

1986年9月至1989年6月中科院武汉数学物理研究所攻读博士学位

1989年6月获博士学位

1989年7月至1996年4月中国科学院武汉数学物理研究所工作，历任助理研究员、副研究员、研究员

1996年入选中国科学院“百人计划”到中科院应用数学所工作

1996年至今在中国科学院数学与系统科学研究院任研究员

现任：

中科院数学与系统科学研究院应用数学研究所所长

中科院数学与系统科学研究院研究员、博士生导师

研究方向

主要从事非线性偏微分方程和非线性变分问题的研究，特别是应用非线性分析，如临界点理论来研究非线性偏微分方程解的存在性，多解性等。

学术访问

1991.09-1992.08 法国巴黎第九大学决策数学研究中心作访问学者

1994.06-1994.09 澳大利亚新南威尔士大学作访问学者

1995.06-1995.08 澳大利亚新南威尔士大学作访问学者

1995.09-1995.11 澳大利亚昆士兰大学作访问学者

1996.04-1997.06 受洪堡基金资助在德国科隆大学和美茵滋大学作洪堡学者

1999.03-1999.06 澳大利亚新南威尔士大学访问教授

2000.06-2000.08 澳大利亚新南威尔士大学访问教授

2001.09-2001.11 澳大利亚新南威尔士大学访问教授

2003.04-2003.06 澳大利亚新南威尔士大学访问教授

2004.05-2004.05 瑞士洛桑高工访问教授

2005.11-2005.12 澳大利亚昆士兰大学访问教授

社会兼职

《应用数学学报》执行编委《数学物理学报》执行编委《Journal of Partial Differential Equations》执行编委《系统科学与数学》执行编委

科研成果

在研项目

1. 杰出青年基金项目：“非线性偏微分方程”，2005-2008

2. 国家自然科学基金重点项目《非线性椭圆与抛物型方程的理论及其应用研究》（批准号10631030，成员, 2007.1-2010.12）

4. 科学院重要方向性项目《数学物理中的若干重大问题》，首席科学家，2007.1--2010.12

已完成项目

百人计划

6. 曾主持国家自然基金项目“无界域上变分形式的非线性椭圆型方程”，1999年-2001年，批准号 19101041

7. 曾主持中科院

论文论著

1. Cao Daomin and Zhu Xiping, 1988, On the existence and nodal character of solutions of semilinear elliptic equations,Acta Mathematicae Scientia，Vol.8,no.3, 345-395.

2. Zhu Xiping and Cao Daomin, 1989, The concentration-compactness principle in nonlinear elliptic equations, Acta Mathematicae Scientia，Vol.9, no.1, 307-323.

3. Cao Daomin, Li Gongbao and Yan Shusen, 1989, Bifurcation for quasilinear equations on R with natural growth conditions, Proceedings of the Royal Society of Edinburgh, Vol.113A,no.3-4, 215-228.

4. Cao Daomin, 1990, Positive solutions and bifurcation from the essential spectrum of a semilinear elliptic equation on R , Nonlinear Analysis TMA , Vol.15,no.11,1045-1052.

5. Cao Daomin, 1991, Bifurcation for quasilinear elliptic system on R with natural growth conditions, Journal of London Mathematical Society, Vol.44, no.3, 514-524.

6. Daomin Cao, 1992, Nontrivial solutions of semilinear elliptic equations with critical exponent in R , Communications in Partial Differential Equations，Vol.17, no.3-4, 407-435.

7. Daomin Cao, 1993, Existence of positive solutions of semilinear elliptic equations in R , Differential and Integral Equations, Vol.6, no.3, 655-661.

8. Cao Daomin and Li Gongbao, 1993, On a variational problem proposed by H.Brezis, Nonlinear Analysis, TMA, Vol.20, no.9, 1145 -1156.

9. Cao Daomin, 1993, Multiple solutions of a Neumann problem in an exterior domain, Communications in Partial Differential Equations, Vol.18, no.3, 687-700.

10. Cao Daomin, 1993, Multiple solutions of a semilinear elliptic equation on R , Ann.Inst.Henri Poincare,Analyse non lineaire,Vol.10,no.6,593-604.

11. Cao Daomin, Li Gongbao and Zhu Huansong, 1994, Multiple solutions of imhomogenous elliptic equations involving critical Sobolev exponent, Proceeding of the Royal Society of Edinburgh, Vol.124A, no.6, 1177-1191.

12. Cao Daomin, 1995, Eigenvalue problems and bifurcations of semilinear elliptic equations in R , Nonlinear Analysis, TMA , Vol.24,no.4,529-554.

13. Cao Daomin, 1995, Positive solutions of a semilinear elliptic equation, Journal of Partial Differential Equations, Vol.8, no.3, 261-272.

14. Cao Daomin and E.S.Noussair, 1995, Multiple positive and nodal solutions for semilinear elliptic equations involving critical Sobolev exponents, Indiana University Mathematics Journal, Vol.44, no.4, 1249-1271.

15. Cao Daomin and Zhou Huansong, 1996, On the existence of multiple solutions of nonhomogenous equations involving critical Sobolev exponent, Z.angew. Math.Phys,， Vol.47, no.1, 89-96.

16. Cao Daomin, Li Gongbao and Zhong Xiao, 1996, A note on the number of nonhomogenous semilinear equations in R , Nonlinear Analysis TMA, Vol.27, no.9, 1095-1108.

17. Daomin Cao and Huansong Zhou, 1996, Multiple positive solutions of nonhomogenous equations in Rn,Proceedings of the Royal Society of Edinburgh, Vol.126A,no.2,443-463.

18. Daomin Cao and E.S.Noussair, 1996, Multiplicity of positive and nodal solutions for nonlinear elliptic problems, Ann Henri Poincare,Analyse non lineaire, Vol.13,no.5,557-588.

19. Daomin Cao and J Chabrowski, 1996, On the number of positive solutions for nonhomogenous semilinear elliptic problems, Advance in Differential Equations, Vol.1, no.5, 753-772.

20. Daomin Cao,E.N.Dancer, E.S.Noussair and Shusen Yan,1996, On the existence and profile of multi-peaked solutions to singularlyperturbed semilinear Dirichlet problems, Discrete and Continuous Dynamical System,Vol.2,no.2,221-236.

21. Daomin Cao, Gongbao Li and Huansong Zhou, 1996, Multiple positive solutions of nonhomogenous elliptic equations, Chinese Ann.Math.,Series A, Vol.17,no.4,475-482.

22. Daomin Cao and J.Chabrowski, 1997, Multiple solutions of nonhomogenous elliptic problems with critical nonlinearity, Differential and Integral Equations, Vol.10, no.5, 791-814.

23. Daomin Cao and Xiao Zhong, 1997, Multiplicity of positive solutions for semilinear elliptic equations involving the critical Sobolev exponents, Nonlinear Analysis TMA, Vol.29, no.4, 461-483.

24. Cao Daomin, E.S.Noussair and Shusen Yan, 1998, Existence and uniquness results on single-peaked solutions of a semilinear problem, Ann.H. Poincare,Analyse non lineaire, Vol.15,no.1, 73-111.

25. E.S.Noussair and Daomin Cao, 1998, Multiplicity results for an inhomogenuous nonlinear elliptic problem, Differential and Integral Equations, Vol.11，no.1, 47-59.

26. Daomin Cao, 1998, A note on the existence of multi-peaked solutions to a semilinear elliptic problem, Advances in Nonlinear Differential Equations and Related Areas, World Scientific.

27. Daomin Cao and T.Kupper, 1999, On the existence of multi-peaked solutions to a semilinear Neumann problem, Duke Mathematical Journal，Vol.97，no.2, 261-300.

29. Daomin Cao and E.S.Noussair, 2000, Multi-peak solutions for a singularly perturbed semilinear elliptic problem, Journal of Differential Equations, Vol.166，266-289

30. Daomin Cao and E.S.Noussair, 2000，Existence of symmetric multi-peaked solutions to singularly perturbed semilinear problems, Communications in Partial Differential Equations，Vol.25，2185-2232

31. Daomin Cao, E.S. Noussair and S. Yan, 2001, Existence and nonexistence of interior-peaked Solution for a nonlinear Neumann problem, Pacific Mathematics Journal, Vol. 200, 19-40.

32. Daomin Cao, M. Lucia and H.S. Zhou, 2001, A Neumann problem in exterior domain,Manuscripta Mathematica，Vol.106, 63-74.

33. Daomin Cao and E.S. Noussair, 2001, The effect of geometry of domain boundary in an elliptic Neumann problem, Advances in Differential Equations，Vol.6, 935-958.

34. Daomin Cao, E.S. Noussair and S.Yan, 2001, Symmetric solutions for a Neumann problem involving critical exponent, Proceedings of the Royal Society of Edinburgh，Vol.131A, 1039-1064.

35. Daomin Cao, E.S. Noussair and S.Yan, 2002, On the scalar curvature equation - u=(1+ K) u in R , Calculus of Variation and Partial Differential Equations , Vol.15,403-419.

36. Daomin Cao and Shuangjie Peng, 2003， A compactness result for singular elliptic problems involving critical Sobolev exponent, Proceedings of the American Mathematical Society, Vol. 131，1857-1866．

37. Daomin Cao and Shuangjie Peng, 2003，The Asymptotic behaviour of the ground state solutions for Henon equation, Journal of Mathematical Analysis and applications, Vol. 278，1-17．

38. Daomin Cao and H.P. Heinz, 2003，Uniqueness of positive multi-lump bound states of nonlinear Schrodinger equations, Mathematische Zeitschrift , Vol 243，599-642

39. Daomin Cao and Pigong Han, 2003, A note on the positive energy solutions for elliptic equations involving critical Sobolev exponents, Applied Mathematics Letters, Vol.16,1105-1113.

40. Daomin Cao and Pigong Han,2004, Solution for semilinear elliptic equations with critical exponents and Hardy potential, Journal of Differential Equations, Vol.205，521-537.

41. Daomin Cao and E.S.Noussair,2004, Multi-bump standing waves with a critical frequency for nonlinear Schrodinger equations, Journal of Differential Equations, Vol.203 , 292--312.

42. Daomin Cao and Pigong Han,2005, High energy positive solution for Neumann problem of an elliptic system of equations with critical nonlinearities, Calculus of Variation and Partial Differential Equations , Vol. 25，161-185.

43. Daomin Cao and Shuangjie Peng, 2006, Multi-bump bouded states of Schrodinger equations with critical frequency, Mathematische Annalen, Vol.336, 925-948.

44. Daomin Cao and Pigong Han, 2006, Solutions to critical elliptic equations with multi-singular inverse square potentials, Journal of Differential Equations, Vol.224,332-372.

45. Daomin Cao and Zhongwei Tang, 2006, Existence and uniqueness of multi-bump bounded sates of nonlinear Schrodinger equations with electromagnetic fields, Journal of Differential Equations, Vol.222, 189-205.

46. Ravi P.Agarwal, Daomin Cao, H.S. and D.O'Regan, 2006, Existence and multiplicity of positive solutions for singular semipostone p-Laplacian equations, Canadian Journal of Mathematics, Vol.58 ,449-475.

47. Daomin Cao and Shuangjie Peng, 2006, Asymptotic behavior for elliptic problems with singular coefficient and nearly critical potential, Ann. Mat. Pura Appl., Vol.185, 189 - 205.

48. X.H.Tang, Daomin Cao and X.F. Zou, 2006, Global attractivity of positive periodic solution to Lotka-Volterra competition systems with pure delay, Journal of Differential Equations, Vol.228, 580-610.

49. Daomin Cao, E.S.Noussair and S.Yan, 2006, Multiplicity of asymptotic solutions for nonlinear elliptic problems, Quarterly of Applied Mathematics, Vol.64，468-482.

50. Sun Chunyou, Daomin Cao and Jinqiao Duan, 2006, Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity, Nonlinearity, Vol.19, 2645-1665.

51. Daomin Cao, E.S.Noussair and S.Yan , Multiscale-bump standing waves with a critical frequency for nonlinear Schrodinger equations, Transaction of American Mathematical Society, to appear.

52. Wei Wang, Daomin Cao and Jinqiao Duan, Effective macroscopic dynamics of stochastic partial differential equations in perforated domains, SIAM Journal of Mathematical Analysis, to appear

53. Sun Chunyou, Daomin Cao and Jinqiao Duan, Uniform attractors for non-autonomous wave equations with nonlinear damping，SIAM Journal on Applied Dynamical Systems, to appear

所获荣誉

1999年中国科学院青年科学家奖一等奖（个人）；

2001年第五届中国科学院杰出青年；

2004年中国科学院优秀指导老师；

2005年中国科学院优秀研究生指导教师奖；

2006年中国科学院研究生院优秀教师

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