The Asymptotic Approximation Of Solutions For Second Order Quasilinear Singularly Perturbed Differential Equations

This thesis mainly makes a study of the Dirichlet Question in the second order quasilin-ear singularly perturbed differential equations. Under appropriate conditions we ensure the existence of solutions, and work out all the asymptotic approximation of equations with the boundary layer function method, afterwards, we get the exponential decay for zero times ap-proximate and time approximation of boundary layer function, again,we get all the boundary layer function exponential decay by induction, Thereby we conclude subtotal of asymptotic approximation solution and the effectiveness of subtotal. Then we use successive approxima-tion method to work out remained estimates for the subtotal.Thus we obtain the uniform of valid asymptotic expansions. At last, we put this conclusion in fact with examples.