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•  Hướng nghiên cứu : 
  
   Phương trình đạo hàm riêng  trong cơ  học, vật l‎ý và hình học, bằng các phương pháp tính biến phân, giải tích phi tuyến và tôpô đại số.
   
• Đã thăm viếng và làm việc tại :
  
  . Université Paris VII, France
  . University of Bonn, Germany
  . University of Heidelberg, Germany
  . The International Centre for Theoretical Physics , Trieste, Italy
  . Universita di Firenze, Firenze, Italy
  . Instituto de Matematicas U.N.A.M., Cuernavaca, Morelos, Mexico
  . Centro de Investigacion en Matematicas, Guanjuato, Mexico
  . The ETH , Zurich, Switzerland
  . International Centre for Mathematical Sciences, Edinburgh, Scotland, UK
  . Ohio University, Athens, Ohio , USA
  . University of Texas at San Antonio, Texas, USA
   
•  Các bài báo toán đã công bố
  
  - D.M. Duc, N.H. Loc, L.L. Phi, Nonlinear versions of Stampacchia and Lax–Milgram theorems and applications to p-Laplace equations . Nonlinear Analysis, Volume 68, Issue 4,  2008,  925-931.
   - D.M.Duc,  N.C. Phuc, N. V. Truyen, Weighted Sobolev's inequalities for bounded domains and singular elliptic equations, Indiana Univ. Math. J. 56 No. 2 (2007), 615-642.
   - D.M. Duc, T.V. Hung and N.T. Khai. Morse - Palais lemma for nonsmooth functionals on normed spaces.  Proceedings AMS, Volume 135, Number 3, March 2007, Pages 921–927.
  - D.M. Duc, T.V. Hung and N.T. Khai. Critical points of non-C2 functionals.  J. Topological Methods in  Nonlinear Analysis, V.29, N.1, 2007, 35-68.
  - D.M. Duc, N. Hoang and L.H. Nguyen. Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming . J. Math. Anal. Appl. 323 (2006) 441-455.
  -  D.M. Duc and N.T. Vu. Nonuniformly elliptic equations of p-Laplacian type . Nonlinear Analysis 61 (2005), 1483 - 1495.
  - L.H. An, P.X. Du, D.M. Duc and P.V. Tuoc. Lagrange multipliers for functions derivable along directions in a linear subspace.  Proc. Amer. Math. Soc 133 (2005), 595-604
  - D.M. Duc, N.L. Luc, L.Q. Nam and T.T Tuyen. Multiple solutions for a nonlinear singular Dirichlet problem in the book Abtract and applied analysis, Proceedings of the International Conference at Ha Noi, 13-17 August 2002, edited by N.M. Chuong, L. Nirenberg and W. Tutschke . World Scientific , Singapore, 2004 .
  -  D.M. Duc, N.H. Loc and P.V. Tuoc. Generalized zeros of operators and applications . Vietnam Journal of Mathematics 32 SI (2004), 87-96.
  - D.M. Duc, N.H. Loc and P.V. Tuoc. Topological degree for a class of operators and applications. Nonlinear Analysis 57 (2004) pp 505-518.
  - D.M.Duc, N.L Luc, L.Q. Nam and T.T.Tuyen. On topological degree for potential operators of class (S)+. Nonlinear Analysis: Theory, Methods and Application 55 (2003), pp. 951-967.
  - P.X. Du and D.M.Duc. A non-homogenuous p-Laplace equation in border case. Acta Math. Vietnam 27 69-75(2002).
  - D.M. Duc . Flows method in global analysis . Acta Math. Vietnam 20 171-180(1995)
  - D.M. Duc . Variational Problems of certain functionals . Internatonal J. Math. 6 503-535(1995)
  - D.M. Duc and N.V. Hieu , Graphs with prescribed mean curvature on Poincaré disk . Bull. London Math. Soc. 27 353-358(1995).
   - D.M. Duc and I.M.C. Salavessa. On a class of quasilinear elliptic equations. Manuscripta Math. 82 227-239(1994).
  - D.M. Duc and N.V. Hieu , Graphs with prescribed mean curvature on hyperpolic spaces . Manuscripta Math. 83 111-121(1994).
  - J.A. Canavati , D.M. Duc and F. Galas-Fontes , Local weighted Poincare inequalities . Appl. Anal. 48 113-121(1993).
  - D.M. Duc and J. Eells . Regularity of exponentially harmonic functions .Inter. J. Math. 2 4(1991), 395-408.
  - D.M. Duc . Complete metrics with nonpositive curvature on the disk .Proceedings Amer. Math.Soc. 113 (1991) , 171-176 .
  - D.M. Duc . Nonlinear singular elliptic equation . London Math. Soc. 40 (1989) , 420-440 .
  - D.M. Duc and L. Dung . Compactness of Imbedding of Sobolev spaces. J. London Math. Soc. 40 (1989), 105-119 .
  - D.M. Duc . A class of strongly degenerate elliptic operators . Bull. Austral.Math. Soc. 39 (1989) , 177-200
  - D.M. Duc . Coercive properties of elliptic-parabolic operator . Applicable Analysis 29 (1988) , 289-300
  - D.M. Duc . Converse to Taylor´s theorem . Math. Nachr. 120 (1985), 309-312 .
  - D.M. Duc . Topological degree of pseudopositive mappings . Acta Math. Vietnam. 9 (1984) , n.2 , 165-172 .
  - D.M. Duc . Measure of noncompactness and spectral theory . Math. Nachr. 115 (1984) , 305-317.
  - D.M. Duc . Analytic contractive vector fields in Frechet spaces . Bull. Austral. Math. Soc. 27 (1983) , 165-184
  - D.M. Duc . Differential calculus in Frechet spaces . Bull. Austral. Math. Soc. 24 (1981) , 93-122 .
  -  D.M. Duc , D.N. Thanh and D.D. Ang . Relative topological degree of setvalue compact vector fields and its applications . J. Math. Anal. Appl. 80 (1981), 406-432 .

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