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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (6): 695-701.doi: https://doi.org/10.1007/s10483-009-0603-z

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Minimizing sequences of variational problems with small parameters

Ming-Kang NI1，2, Wu-Zhong LIN1，2   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200062, P. R. China;
    2. Division of Computational Science, E-Institute of Shanghai Universities at SJTU,Shanghai 200030, P. R. China
  • Received:2008-12-28 Revised:2009-04-13 Online:2009-06-01 Published:2009-06-01

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Abstract: A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.

Key words: small parameter, variational problem, minimizing sequence

2010 MSC Number: 

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