On singular singularly perturbed initial value problems. (English) Zbl 0676.34038

The singular system \(\epsilon z'(t)=F(z,t,\epsilon)\) with a small \(\epsilon >0\) and give z(0) is solved under certain assumptions in a finite interval [0,T] up to an O(\(\epsilon)\) in the case that F(Z,t,0) has an infinite family of solutions Z(t). The investigation combines the methods of A. B. Vasileva and V. F. Butuzov [Singularly perturbed equations in the critical case, Moscow State Univ. (1978)] with those of R. E. O’Malley and J. E. Flaherty [SIAM J. Appl. Math. 38, 225-248 (1980; Zbl 0471.65056)] and simplifies them. Eight striking examples are given.
Reviewer: L.Berg


34E15 Singular perturbations for ordinary differential equations
34E20 Singular perturbations, turning point theory, WKB methods for ordinary differential equations
34C45 Invariant manifolds for ordinary differential equations


Zbl 0471.65056
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