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Zbl 0759.39006
Zdun, Marek Cezary
On diffeomorphic solutions of simultaneous Abel's equations. (English)
[J] Arch. Math., Brno 27a, 123-131 (1991). ISSN 0044-8753

Let $f\sb 1,f\sb 2,\dots,f\sb N$ be given continuous bijections of an interval $(a,b)$, $-\infty\le a<b\le\infty$, onto itself and let $c\sb 1=1$, $c\sb i\ne 0$, $i=2,\dots,N$. The problem of existence of $C\sp r$- solutions $\varphi:(a,b)\to R$ of the system of simultaneous Abel's equations $\varphi(f\sb i(x))=\varphi(x)+c\sb i$, $i=1,2,\dots,N$, $x\in(a,b)$, is considered and conditions on $f\sb 1$, $f\sb 2,\dots,f\sb N$ are given which ensure the existence of $C\sp r$-diffeomorphic solutions of the system of Abel's equations.
[H.L.Vasudeva (Chandigarh)]

MSC 2000:: *39B12 Iteraterative functional equations
34K99 Functional-differential equations

Keywords: diffeomorphic solution; functional equation; differential equation with deviating argument; iterations; continuous fraction; system of Abel's equations

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