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On solvability of quasilinear boundary value problems for systems of generalized ordinary differential equations. (Russian. English summary) Zbl 0686.34022

Sufficient conditions for the existence and for the unique existence of a solution to the problem \(dx_ i(t)=f_ i(t,x_ 1(t),...,x_ n(t))\) \(d\alpha_ i(t)\), \(a\leq t\leq b\), \(h_ i(x_ 1,...,x_ n)=c_ i(x_ 1,...,x_ n)\), \(i=1,2,...,n\) are given where \(\alpha_ i: [a,b]\to R\) are nondecreasing functions, \(f_ i\) satisfy locally Carathéodory conditions and \(h_ i(x)=\sum^{n}_{k=1}\int^{b}_{a}x_ k(\tau)d\beta_{ik}(\tau),\) \(i=1,...,n\) for \(x\in BV_ n(a,b)\) (vector functions of bounded variation on [a,b]) with \(\beta_{ik}\in BV_ n(a,b)\), \(c_ i: BV_ n(a,b)\to R\) are continuous mappings.
Reviewer: W.Seda

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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