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