A Class of Nonlinear Boundary Value Problems for the Sceond-Order <em>E</em><sub>2</sub> Class Elliptic Systems in General Form

LI Ming-zhong; XU Ding-hua

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LI Ming-zhong, XU Ding-hua. A Class of Nonlinear Boundary Value Problems for the Sceond-Order E2 Class Elliptic Systems in General Form[J]. Applied Mathematics and Mechanics, 2003, 24(2): 146-162.

Citation:

LI Ming-zhong, XU Ding-hua. A Class of Nonlinear Boundary Value Problems for the Sceond-Order E₂ Class Elliptic Systems in General Form[J]. Applied Mathematics and Mechanics, 2003, 24(2): 146-162.

LI Ming-zhong, XU Ding-hua. A Class of Nonlinear Boundary Value Problems for the Sceond-Order E2 Class Elliptic Systems in General Form[J]. Applied Mathematics and Mechanics, 2003, 24(2): 146-162.

Citation:

LI Ming-zhong, XU Ding-hua. A Class of Nonlinear Boundary Value Problems for the Sceond-Order E₂ Class Elliptic Systems in General Form[J]. Applied Mathematics and Mechanics, 2003, 24(2): 146-162.

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A Class of Nonlinear Boundary Value Problems for the Sceond-Order E₂ Class Elliptic Systems in General Form

LI Ming-zhong¹,
XU Ding-hua^1,2

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 Date: 2001-07-24
Rev Recd Date: 2002-10-17
Publish Date: 2003-02-15

Abstract

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.
- elliptic systems,
- boundary value problems,
- singular integral equations,
- singular integral operators,
- existence

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References(7)

References

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