Dirichlet problem of nonlinear second order partial differential equations resolved with any derivatives

In this paper we will discuss the Dirichlet problem of nonlinear second order partial differential equations resolved with any derivatives. First, we transform it into generalized integral equations. Next, we discuss the existence of the classical solution by Leray-Schauder degree and Sobolev space\ $H^{-m_1}({\mathrm{\Omega }}_1)$.