曹道民

人物关系

丁夏畦

老师

生平经历

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

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

研究方向

目前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。

主要奖励

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

科研项目

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）

3. 973项目《数学与其它领域交叉的若干专题》子项目"流体力学与材料科学中的偏微分方程"课题组成员，2007- -2010

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

1. 曾参加由丁夏畦院士主持的中科院重大项目"数学物理方程"的研究工作，是主要成员，项目已顺利完成

2. 曾主持国家自然基金(青年)项目"无界域上变分形式的非线性椭圆型方程"，1992年-1994年，批准号 19101041

3. 曾独立完成武汉市首届科技晨光计划项目"非线性椭圆型方程解的存在性研究"，1993年-1995年，项目编号93CGA

4. 曾参加国家自然基金项目"某些变分形式的拟线性椭圆型方程研究"，为主要成员，1996年-1998年

5. 得到中科院"百人计划"资助，1997年-1999年，终期评估时被科学院评为优秀，得到奖励

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. 曾主持中科院院长基金特别支持项目"非线性椭圆型方程解的研究"，2000年---2001年

8. 参加973项目"核心数学的若干前沿问题", 是子项目"非线性偏微分方程"课题组成员，1999- 2004

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.

28. Daomin Cao,E.S.Noussair and S.Yan, 1999, Solutions with multiple "peaks" for nonlinear elliptic equations, Proceedings of the Royal Society of Edinburgh，Vol.126A, 235-264.

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

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

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

参考资料

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