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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
##### Keywords:
locally Carathéodory conditions