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Singularly perturbed boundary value problems with angular limiting solutions

Author: F. A. Howes
Journal: Trans. Amer. Math. Soc. 241 (1978), 155-182
MSC: Primary 34D15
MathSciNet review: 0499510
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Abstract: A basic result of Haber and Levinson which describes the behavior of solutions of $ \varepsilon y'' = f(t,y,y')$,$ a < t < b$, $ y(a,\varepsilon )$, $ y(b,\varepsilon )$, prescribed, in the presence of a reduced solution with corners is modified to treat related classes of problems. Under various stability assumptions, solutions are shown to remain, for small $ \varepsilon \, > \,0$, in a o(l)-neighborhood of an angular reduced solution with the possible exception of narrow layers near the boundaries in some cases. Each aspect of the theory developed here is illustrated by several examples.

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