Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (2): 163-181.

• Articles • Previous Articles     Next Articles

A CLASS OF NONLINEAR BOUNDARY VALUE PROBLEMS FOR THE SECOND-ORDER E2 CLASS ELLIPTIC SYSTEMS IN GENERAL FORM

LI Ming-zhong1, XU Ding-hua1,2   

  1. 1. Department of Mathematics, Shanghai University, Shanghai 200436, P.R.China;
    2. Department of Computational Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, P.R.China
  • Received:2001-07-24 Revised:2002-10-17 Online:2003-02-18 Published:2003-02-18
  • Supported by:

    the National Natural Science Foundation of China (19671056);Shanghai Municipal Natural Scientific Foundation (99ZA14030, 01ZA14023);Jiangxi Provincial Natural Scientific Foundation (981102, 0211014)

Abstract: A class of nonlinear boundary value problems (BVP) for the second-order E2 class elliptic systems in general form is discussed. By introducing a kind of transformation,this kind of BVP is reduced to a class of generalized nonlinear Riemann-Hilbert BVP. And then some singular integral operators are introduced to establish the equivalent nonlinear singular integral equations. The solvability is proved under some suitable hypotheses by means of the properties of singular integral operators and the function theoretic methods.

2010 MSC Number: 

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