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