The Dirichlet problem for a quasilinear singularly perturbed second order system (Q5905384)

The authors consider solutions exhibiting boundary-layer behavior for the vector differential equation \(\varepsilon d^ 2x/dt^ 2 = f(t,x, \varepsilon) dx/dt + g(x,t, \varepsilon)\), \(0<t<1\), for small values of \(\varepsilon\), and with Dirichlet boundary conditions. An existence proof is given for this type of solution.