Abstract
In this paper we study nonlinear Riemann-Hilbert problems for the first order quasilinear elliptic system with the general form. Because its equivalent form is nonlinear singular integral equation and the boundary condition is strongly nonlinear, so its proof is more difficult. We overcome these difficulties by means of the results which are got by V. S. Vinogradov and me in the papers[1,2] and integral equation theory. We have proved the existence theorem of the solution for the BVP, which generalize the results of nonlinear Riemann-Hilbert problem for the analytic function and first order elliptic system[3–5]. Key wordsNonlinear Riemann-Hilbert problemnonlinear singular integral equationexistence theorem
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