ON PSEUDO-RIEMANN-HILBERT PROBLEM FOR COMPLEX OVERDETERMIND PARTIAL DIFFERENTIAL SYSTEMS OF FIRST ORDER

Suppose Gj= {zj||zj|【1}, Gj= {zj||zj|=1},j= 1,2, G1 = {z1|ε【 |z1|【1},where εisa constant, 0 【ε【1 . We consider the pseudo-Riemann-Hilbert problem;We assume that（i） λis a H lder continuous function on G1× G2, and λ≠0; γis a real H lder continuous functionon G1× G2, and let Hβ（γ） be its bound.（ii） fj is continuous with respect to （z1 ,z2） ∈ 1z× 2 and is holomorphic with respect to W ∈BR ={W||W|≤R, B is a positive constant}; fi satisfies compatibility condition.（iii） and and continuous with respect to （z1,z2, W） ∈ 1× 2× BR; f1,f2, and satisfyLipschitz condition with respect to W ∈BR, and let LR be the Lipschitz constant and KR be their bound.