The estimation of solution of the boundary value problem of the systems for quasi-linear ordinary differential equations (Q1206690)

The author considers the singular perturbation of the boundary value problem for a system of quasilinear ordinary differential equations \(x'=f(t,x,y,\varepsilon)\), \(\varepsilon y''=g(t,x,y,\varepsilon)y'+h(t,x,y,\varepsilon)\), \(x(0,\varepsilon)=A(\varepsilon)\), \(y(0,\varepsilon)=B(\varepsilon)\), \(y(1,\varepsilon)=C(\varepsilon)\), where \(x,y,f,h,A,B,C\in R^ n\), and \(g\) is an \(n\times n\) matrix function. The asymptotic expansion of the solution is constructed, and its remainder term is estimated, by applying the diagonalization technique and the fixed point theorem.