Initial Layer Phenomena for a Class of Singular Perturbed Nonlinear System with Slow Variables

The initial layer phenomena for a class of singular perturbe d nonlinear system with slow variables are studied.By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different "thickness",the N-order approximate expansion of perturbed solution concerning small parameter is obtained,and the "multiple layer" phenomena of perturbed solutins are revealed.Using the fixed point theorem,the existence of perturbed solution is proved,and the uniformly valid asymptotic expansion of the solutions is given as well.