The higher order approximation of solutions of quasilinear second order systems for singular perturbation (Q1093068)

Using the theory of invariant region, the author considers the existence and the asymptotic behavior of solution of vector second order quasilinear boundary value problem: \[ ey''=f(x,y,\epsilon)y'+g(x,y,\epsilon),\quad y(0,\epsilon)=A(\epsilon),\quad y(1,\epsilon)=B(\epsilon) \] as the positive perturbation parameter \(\epsilon\) tends to zero, where y, g, A and B are vector-valued and f is a matrix function. Under the appropriate assumptions the author obtains, involving the boundary layer, uniformly valid asymptotic solutions of higher order approximation.