Boundary and angular layer behavior in singular perturbed quasilinear systems

In this paper, using the method of differential inequalities, we study the existence of solutions and their asymptotic behavior, as 0⁺, of Dirichlt problem for second order quasilinear systems. Depending on whether the reduced solutionu(t) has or does not have a continuous first-derivative in (a, b), we study two types of asymptotic behaviour, thus leading to the phenomena of boundary and angular layers.