Abstract: The discontinuous boundary value problem of quasilinear mixed type equations of second order in a much more general domain is discussed by using the method of complex analysis with a deformation such that the boundary curves of the hyperbolic domain are transformed onto the segments, and then, the solvable results in the more general domains are obtained, which are generalizations of the recent results in articles.

Key words: Discontinuous boundary value problem, Quasilinear mixed equation, Successive iteration, Hyperbolic domain