Journal of East China Normal University(Natural Sc ›› 2008, Vol. 2008 ›› Issue (5): 72-77,8.

• Article • Previous Articles     Next Articles

Dirichlet problem of semi linear singular perturbation elliptic equations(Chinese)

ZHU Zhen-bo1,2, NI Ming-kang1,2

  

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062,China; 2. Division of Computational Science, E-Institute of Shanghai Universities,SJTU,Shanghai 200030,China
  • Received:2007-07-07 Revised:2007-10-22 Online:2008-09-25 Published:2008-09-25
  • Contact: NI Ming-kang

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Abstract:

Using transformation of coordinates of M.Vishik and L.Lyusternik, the method of boundary function was used to construct the uniformly valid asymptotic solutions of the Dirichlet problem of semi-linear singular perturbation elliptic equations.Under the uniformly valid asymptotic solutions obtained,the upper and lower solutions were constructed which satisfied the condition of Amann and guranteed the existence of the solution.Finally,the reminder estimation was made.

Key words: elliptic equation, boundary functions, upper and lower solutions, reminder estimation, singular perturbation, elliptic equation, boundary functions, upper and lower solutions, reminder estimation

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