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Singular perturbation of some higher order quasilinear two point boundary value problems. (Chinese. English summary) Zbl 0758.34043

Summary: We consider the boundary value problem \[ \varepsilon y^{(n)}=f_ 1(t,\varepsilon,y,\dots,y^{(n-2)})y^{(n-1)}+f_ 2(t,\varepsilon,y,\dots ,y^{(n-2)}),\quad 0<t<1, \] \(y^{(j)}(0,\varepsilon)=A_ j(\varepsilon)\), \(j=0,1,\dots,n-2\), \(y^{(n-2)}(1,\varepsilon=B(\varepsilon)\), where \(\varepsilon\) is a small positive parameter. Under some suitable assumptions, using the method of “boundary layer corrections” and the differential inequality techniques, we obtain a uniformly efficient asymptotic solution which includes the boundary layer and can be approximated any times.

MSC:

34E15 Singular perturbations for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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