×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite