Singular perturbation of two point boundary value problems in nonlinear systems of higher order. (Chinese. English summary) Zbl 0758.34044

Chen, Xiu

Appl. Math., J. Chin. Univ. 6, No. 1, 100-109 (1991).

Summary: Using the method and technique of differential inequalities, we study the existence and asymptotic behavior, as \(\varepsilon\to 0^ +\), of the solutions of vector boundary value problems for \(0<t<1\) \[ \varepsilon y^{(n)}=f(t,y,y',\dots,y^{(n-1)},\varepsilon),\;y^{(j)}(0,\varepsilon)=A_ j(\varepsilon)\;(0\leq j\leq n-2),\;y^{(n- 2)}(1,\varepsilon)=B(\varepsilon). \] Two types of asymptotic behavior are studied depending on whether the reduced solution has a continuous \((n- 1)\)th-order derivative in (0,1) or not, leading to the phenomena of boundary and angular layers.

MSC:

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

Keywords:

technique of differential inequalities; existence; asymptotic behavior; vector boundary value problems; boundary and angular layers