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Hysteresis in singular perturbation problems with nonuniqueness in limit equation. (English) Zbl 0793.34040
Visintin, A. (ed.), Models of hysteresis. Proceedings of a workshop, held in Trento, Italy in September 1991. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 286, 91-101 (1993).
We investigate a problem (1) $$u_ \varepsilon(a)=\zeta_ \varepsilon$$, $$\varepsilon u_ \varepsilon'(t)+F(u_ \varepsilon(t))=z_ \varepsilon(t)$$ for a.e. $$t \in (a,b)$$, where $$\varepsilon \geq 0$$ is a parameter, $$(a,b)$$ is a bounded interval in $$R$$, $$\zeta_ \varepsilon \in R$$ and $$z_ \varepsilon \in L^ \infty (a,b)$$. The main goal is the study of the convergence (or compactness) of the solutions $$u_ \varepsilon$$ to (1) as $$\varepsilon \to 0+$$ provided that the $$z_ \varepsilon$$’s are convergent (or compact) in an appropriate sense.
For the entire collection see [Zbl 0785.00016].

MSC:
 3.4e+16 Singular perturbations for ordinary differential equations